feat(vision): resolve persisted image URLs against the API base

Images are now stored on disk under tmp (not SQLite) and served via
GET /images/:conversationId/:imageId. Persisted ImageChunk.url is a compact
relative HTTP path (/images/<conv>/<uuid>.png) instead of a base64 data URL.
No wire/transport-contract type change (behavior only) — re-mirrored the
delta notes.

- New pure resolveImageUrl(url, apiBase) helper (core/chunks/image-url.ts,
  +8 tests): data/absolute URLs pass through; relative paths are prepended
  with the API base (no double slash; empty base -> root-relative). Exported
  from core/chunks + re-exported from features/chat.
- ChatView: new apiBaseUrl prop; <img src> uses resolveImageUrl. The
  optimistic echo's data URL passes through; persisted relative paths
  resolve against the base. +3 tests.
- AppStore exposes httpBase (getter); App.svelte passes apiBaseUrl into
  ChatView and the heartbeat RunModal (also renders image chunks).

Verification: svelte-check 0/0; vitest 959/959 (run twice, +11); biome
clean; vite build OK. See backend-handoff.md §2j-update-2.

Not merged or pushed.

9 files changed, 168 insertions, 5 deletions

diff --git a/src/app/App.svelte b/src/app/App.svelte
index f41d7ba..7d70f67 100644
--- a/src/app/App.svelte
+++ b/src/app/App.svelte
@@ -516,6 +516,7 @@
 							onShowEarlier={handleShowEarlier}
 							thinkingKeyBase={store.activeChat.thinkingKeyBase}
 							providerRetry={store.activeChat.providerRetry}
+							apiBaseUrl={store.httpBase}
 						/>
 					{/key}
 				</div>
@@ -610,6 +611,7 @@
 			closeChat={closeRunChat}
 			stopRun={stopHeartbeatRun}
 			onClose={() => (heartbeatRun = null)}
+			apiBaseUrl={store.httpBase}
 		/>
 	{/key}
 {/if}
diff --git a/src/app/store.svelte.ts b/src/app/store.svelte.ts
index 554d5e0..8353820 100644
--- a/src/app/store.svelte.ts
+++ b/src/app/store.svelte.ts
@@ -157,6 +157,12 @@ export interface AppStore {
   readonly activeConversationId: string | null;
   /** The workspace currently in view (URL slug); tabs are filtered to it. */
   readonly activeWorkspaceId: string;
+  /**
+   * The resolved HTTP API base URL (e.g. `http://localhost:24203`). Used to
+   * resolve relative image URLs served by the backend (`/images/…`) into
+   * absolute URLs for `<img src>`.
+   */
+  readonly httpBase: string;
   readonly activeChat: ChatStore;
   readonly models: readonly string[];
   /** Per-model metadata (contextWindow, etc.) from `GET /models`. */
@@ -1127,6 +1133,9 @@ export function createAppStore(opts?: CreateAppStoreOptions): AppStore {
     get activeWorkspaceId(): string {
       return activeWorkspaceId;
     },
+    get httpBase(): string {
+      return httpBase;
+    },
     setActiveWorkspace(workspaceId: string): void {
       activeWorkspaceId = workspaceId;
       // Reset to a fresh draft scoped to the new workspace so a new chat is
diff --git a/src/core/chunks/image-url.test.ts b/src/core/chunks/image-url.test.ts
new file mode 100644
index 0000000..8a79c09
--- /dev/null
+++ b/src/core/chunks/image-url.test.ts
@@ -0,0 +1,46 @@
+import { describe, expect, it } from "vitest";
+import { resolveImageUrl } from "./image-url";
+
+const BASE = "http://localhost:24203";
+
+describe("resolveImageUrl", () => {
+  it("returns a data URL as-is (the optimistic echo / a pasted image)", () => {
+    const dataUrl = "data:image/png;base64,iVBORw0KGgo=";
+    expect(resolveImageUrl(dataUrl, BASE)).toBe(dataUrl);
+  });
+
+  it("returns an absolute http URL as-is", () => {
+    const abs = "https://example.com/img.png";
+    expect(resolveImageUrl(abs, BASE)).toBe(abs);
+  });
+
+  it("prepends the api base to a relative /images/ path", () => {
+    expect(resolveImageUrl("/images/conv-123/abc-456.png", BASE)).toBe(
+      "http://localhost:24203/images/conv-123/abc-456.png",
+    );
+  });
+
+  it("does not double the slash when the base has a trailing slash", () => {
+    expect(resolveImageUrl("/images/c/x.png", "http://localhost:24203/")).toBe(
+      "http://localhost:24203/images/c/x.png",
+    );
+  });
+
+  it("adds a leading slash to a path-relative url without one", () => {
+    expect(resolveImageUrl("images/c/x.png", BASE)).toBe("http://localhost:24203/images/c/x.png");
+  });
+
+  it("returns the relative path as-is when apiBase is empty (root-relative)", () => {
+    // A browser resolves a root-relative `/images/…` against the document origin.
+    expect(resolveImageUrl("/images/c/x.png", "")).toBe("/images/c/x.png");
+  });
+
+  it("handles a relative path with an empty apiBase (path-relative without slash)", () => {
+    expect(resolveImageUrl("images/c/x.png", "")).toBe("/images/c/x.png");
+  });
+
+  it("returns a data URL as-is even with an empty apiBase", () => {
+    const dataUrl = "data:image/jpeg;base64,AAAA";
+    expect(resolveImageUrl(dataUrl, "")).toBe(dataUrl);
+  });
+});
diff --git a/src/core/chunks/image-url.ts b/src/core/chunks/image-url.ts
new file mode 100644
index 0000000..e5ec756
--- /dev/null
+++ b/src/core/chunks/image-url.ts
@@ -0,0 +1,35 @@
+/**
+ * Resolve an `ImageChunk.url` into a renderable `<img src>` value.
+ *
+ * Persisted image chunks now carry a COMPACT HTTP path
+ * (`/images/<conversationId>/<uuid>.png`) served by the backend — NOT a base64
+ * data URL (images are stored on disk under tmp, not in the conversation store,
+ * to keep SQLite payloads small). The optimistic echo (what the FE just sent in
+ * `ChatRequest.images`) still carries a data URL, and a chunk could also carry
+ * an absolute `http(s)://` URL, so the resolution is format-aware:
+ *
+ * - `data:` URL  → returned as-is (the optimistic echo / a pasted data URL).
+ * - `http(s)://` → returned as-is (an absolute URL already).
+ * - anything else (a relative path like `/images/…`) → `apiBase` is prepended
+ *   (with no double slash). An empty `apiBase` leaves a root-relative path,
+ *   which a browser resolves against the document origin.
+ *
+ * Pure: input → output, zero DOM, zero Svelte.
+ *
+ * @param url      The chunk's `url` (data URL, absolute, or relative path).
+ * @param apiBase  The HTTP API base URL (e.g. `http://localhost:24203`).
+ */
+export function resolveImageUrl(url: string, apiBase: string): string {
+  if (url.startsWith("data:") || url.startsWith("http://") || url.startsWith("https://")) {
+    return url;
+  }
+  // A relative path (e.g. `/images/…`) — normalize to a leading slash and
+  // prepend the api base. With an empty base this yields a root-relative path
+  // (a browser resolves `/images/…` against the document origin).
+  const path = url.startsWith("/") ? url : `/${url}`;
+  if (apiBase.length === 0) return path;
+  // Join without a double slash: strip a trailing slash from the base, then
+  // append the (leading-slash) path verbatim.
+  const base = apiBase.endsWith("/") ? apiBase.slice(0, -1) : apiBase;
+  return `${base}${path}`;
+}
diff --git a/src/core/chunks/index.ts b/src/core/chunks/index.ts
index eea2303..bdd6ce4 100644
--- a/src/core/chunks/index.ts
+++ b/src/core/chunks/index.ts
@@ -1,5 +1,6 @@
 export type { RenderGroup, ToolBatchEntry } from "./groups";
 export { groupRenderedChunks } from "./groups";
+export { resolveImageUrl } from "./image-url";
 export {
   appendUserMessage,
   applyHistory,
diff --git a/src/features/chat/index.ts b/src/features/chat/index.ts
index 8694691..773cb91 100644
--- a/src/features/chat/index.ts
+++ b/src/features/chat/index.ts
@@ -4,7 +4,7 @@ export type {
   RenderGroup,
   ToolBatchEntry,
 } from "../../core/chunks";
-export { groupRenderedChunks, viewProviderRetry } from "../../core/chunks";
+export { groupRenderedChunks, resolveImageUrl, viewProviderRetry } from "../../core/chunks";
 export type { TurnMetricsEntry } from "../../core/metrics";
 export { isVisionModel } from "./model-select";
 export type { ChatTransport, HistorySync, HistoryWindow, MetricsSync } from "./ports";
diff --git a/src/features/chat/ui.test.ts b/src/features/chat/ui.test.ts
index b0aa6f0..5f8067d 100644
--- a/src/features/chat/ui.test.ts
+++ b/src/features/chat/ui.test.ts
@@ -628,6 +628,58 @@ describe("ChatView", () => {
     expect(img?.getAttribute("loading")).toBe("lazy");
   });
 
+  it("resolves a persisted image chunk's relative url against apiBaseUrl", () => {
+    // Persisted image chunks now carry a compact relative path (`/images/…`)
+    // served by the backend — prepend the API base to render them.
+    const chunks: RenderedChunk[] = [
+      {
+        seq: 1,
+        role: "user",
+        chunk: { type: "image", url: "/images/conv-123/abc-456.png", mimeType: "image/png" },
+        provisional: false,
+      },
+    ];
+
+    const { container } = render(ChatView, {
+      props: { chunks, apiBaseUrl: "http://localhost:24203" },
+    });
+
+    expect(container.querySelector("img")?.getAttribute("src")).toBe(
+      "http://localhost:24203/images/conv-123/abc-456.png",
+    );
+  });
+
+  it("passes a data URL through unchanged even with apiBaseUrl set (optimistic echo)", () => {
+    // The optimistic echo (what the FE just sent) is still a data URL; it must
+    // NOT be mangled by the base-URL prepend.
+    const dataUrl = "data:image/png;base64,iVBOR=";
+    const chunks: RenderedChunk[] = [
+      { seq: null, role: "user", chunk: { type: "image", url: dataUrl }, provisional: true },
+    ];
+
+    const { container } = render(ChatView, {
+      props: { chunks, apiBaseUrl: "http://localhost:24203" },
+    });
+
+    expect(container.querySelector("img")?.getAttribute("src")).toBe(dataUrl);
+  });
+
+  it("leaves a relative image url root-relative when apiBaseUrl is absent", () => {
+    // No apiBaseUrl → a browser resolves `/images/…` against the document origin.
+    const chunks: RenderedChunk[] = [
+      {
+        seq: 1,
+        role: "user",
+        chunk: { type: "image", url: "/images/conv-1/x.png" },
+        provisional: false,
+      },
+    ];
+
+    const { container } = render(ChatView, { props: { chunks } });
+
+    expect(container.querySelector("img")?.getAttribute("src")).toBe("/images/conv-1/x.png");
+  });
+
   it("renders a multi-chunk user message [text, image] and a transcription text", () => {
     // A non-vision model: the server persists the original image chunk AND a
     // transcription text chunk in the SAME user message — render both.
diff --git a/src/features/chat/ui/ChatView.svelte b/src/features/chat/ui/ChatView.svelte
index 8081951..cd69071 100644
--- a/src/features/chat/ui/ChatView.svelte
+++ b/src/features/chat/ui/ChatView.svelte
@@ -1,6 +1,6 @@
 <script lang="ts">
   import type { TurnProviderRetryEvent } from "@dispatch/wire";
-  import { groupRenderedChunks, type RenderedChunk, viewProviderRetry } from "../index";
+  import { groupRenderedChunks, resolveImageUrl, type RenderedChunk, viewProviderRetry } from "../index";
   import {
     interleaveTurnMetrics,
     viewCacheRate,
@@ -24,6 +24,7 @@
     onShowEarlier,
     thinkingKeyBase = 0,
     providerRetry = null,
+    apiBaseUrl = "",
   }: {
     chunks: readonly RenderedChunk[];
     turnMetrics?: readonly TurnMetricsEntry[];
@@ -44,6 +45,14 @@
      * newest attempt + delay, and is cleared when content resumes / turn ends.
      */
     providerRetry?: TurnProviderRetryEvent | null;
+    /**
+     * The HTTP API base URL (e.g. `http://localhost:24203`). Persisted image
+     * chunks carry a compact relative path (`/images/<conv>/<uuid>.png`); this
+     * base is prepended to render them. The optimistic echo's data URL and any
+     * absolute URL pass through unchanged (see `resolveImageUrl`). Defaults to
+     * "" (root-relative — a browser resolves `/images/…` against its origin).
+     */
+    apiBaseUrl?: string;
   } = $props();
 
   // True while a show-earlier page-in is awaited (disables the button).
@@ -96,15 +105,17 @@
 {#snippet chunkRow(rendered: RenderedChunk)}
   {#if rendered.role === "user"}
     <!-- User: a speech bubble, left-aligned. A user message may be multi-chunk
-         ([text, image, image, …]); each chunk renders in its own bubble (the
-         image's url is a base64 data URL or an https URL — render it directly). -->
+         ([text, image, image, …]); each chunk renders in its own bubble. A
+         persisted image chunk's url is a compact relative path (`/images/…`)
+         served by the backend — resolve it against the API base. The
+         optimistic echo's data URL (and any absolute URL) passes through. -->
     <div class="chat chat-start">
       <div class="chat-bubble chat-bubble-primary">
         {#if rendered.chunk.type === "text"}
           <p>{rendered.chunk.text}</p>
         {:else if rendered.chunk.type === "image"}
           <img
-            src={rendered.chunk.url}
+            src={resolveImageUrl(rendered.chunk.url, apiBaseUrl)}
             alt={rendered.chunk.mimeType ?? "pasted image"}
             loading="lazy"
             decoding="async"
diff --git a/src/features/heartbeat/ui/RunModal.svelte b/src/features/heartbeat/ui/RunModal.svelte
index a4ed356..92068ae 100644
--- a/src/features/heartbeat/ui/RunModal.svelte
+++ b/src/features/heartbeat/ui/RunModal.svelte
@@ -11,6 +11,7 @@
 		closeChat,
 		stopRun,
 		onClose,
+		apiBaseUrl = "",
 	}: {
 		/** The run to display (its conversation's chat is shown live). */
 		run: HeartbeatRunView;
@@ -26,6 +27,11 @@
 		/** Stop the heartbeat run (`POST .../runs/:runId/stop`). */
 		stopRun: StopHeartbeatRun;
 		onClose: () => void;
+		/**
+		 * The HTTP API base URL, to resolve persisted image chunk URLs
+		 * (`/images/…`) in the run's transcript. Defaults to "" (root-relative).
+		 */
+		apiBaseUrl?: string;
 	} = $props();
 
 	// Open the live watch ONCE on mount (the modal is keyed per run.id, so a run
@@ -153,6 +159,7 @@
 						onShowEarlier={chat.showEarlier}
 						thinkingKeyBase={chat.thinkingKeyBase}
 						providerRetry={chat.providerRetry}
+						apiBaseUrl={apiBaseUrl}
 					/>
 				{/if}
 			</div>