feat(lsp,cwd): LSP integration + per-conversation cwd; fix cache-warming cache bust

LSP + per-conversation CWD feature:
- new bundled `lsp` extension: hand-rolled JSON-RPC codec (framing/rpc), lazy
  one-server-per-(serverID,root), per-cwd config resolution, on-demand `lsp` tool
- `conversation-store`: getCwd/setCwd (cwdKey); `session-orchestrator` defaults a
  turn's cwd from the store
- `transport-http`: cwd + lsp status endpoints; wire types in transport-contract
- host-bin: register lsp; config wiring

Cache-warming fix (the warm read 0% on the first reheat after a message):
- warm assembled tools under a different cwd than the real turn (a reheat sends no
  cwd, and the warm service had no store fallback). The skills filter rewrites the
  cwd-sensitive `load_skill` description, so the tools block — the first bytes of
  the prompt-cache prefix — diverged and the cache missed entirely. Warm now
  resolves cwd as opts.cwd ?? conversationStore.getCwd(), mirroring handleMessage.
- capture warm sends as `provider.request` spans flagged `warm:true` (thread a
  child logger into providerOpts) so warm vs real bodies are diffable (obs §3.1).
- kernel logger: span-close now merges child-bound attrs like span-open, so a
  `warm:true` query finds the closed span (with usage/status), not just the open.

Tests: warm forwards a warm-flagged logger; warm falls back to stored cwd; logger
open/close attr consistency. Full suite green (873).

3 files changed, 66 insertions, 0 deletions

diff --git a/packages/conversation-store/src/keys.ts b/packages/conversation-store/src/keys.ts
index 0ba25d8..e7204db 100644
--- a/packages/conversation-store/src/keys.ts
+++ b/packages/conversation-store/src/keys.ts
@@ -45,3 +45,7 @@ export function parseMetricsOrdinal(key: string): number {
 	const n = Number.parseInt(last, 10);
 	return Number.isNaN(n) ? -1 : n;
 }
+
+export function cwdKey(conversationId: string): string {
+	return `conv:${conversationId}:cwd`;
+}
diff --git a/packages/conversation-store/src/store.test.ts b/packages/conversation-store/src/store.test.ts
index a82b4cc..49b0e58 100644
--- a/packages/conversation-store/src/store.test.ts
+++ b/packages/conversation-store/src/store.test.ts
@@ -750,3 +750,49 @@ describe("ConversationStore reconcile.repair span", () => {
 		}
 	});
 });
+
+describe("ConversationStore cwd", () => {
+	let storage: StorageNamespace;
+
+	beforeEach(() => {
+		storage = createMemoryStorage();
+	});
+
+	it("setCwd then getCwd returns the value", async () => {
+		const store = createConversationStore(storage);
+		await store.setCwd("conv1", "/home/user/project");
+		const result = await store.getCwd("conv1");
+		expect(result).toBe("/home/user/project");
+	});
+
+	it("getCwd returns null when never set", async () => {
+		const store = createConversationStore(storage);
+		const result = await store.getCwd("conv_unknown");
+		expect(result).toBeNull();
+	});
+
+	it("setCwd is an upsert (second set overwrites)", async () => {
+		const store = createConversationStore(storage);
+		await store.setCwd("conv1", "/first/path");
+		await store.setCwd("conv1", "/second/path");
+		const result = await store.getCwd("conv1");
+		expect(result).toBe("/second/path");
+	});
+
+	it("cwd persists across a fresh store instance on the same db file", async () => {
+		const store1 = createConversationStore(storage);
+		await store1.setCwd("conv1", "/persisted/path");
+
+		const store2 = createConversationStore(storage);
+		const result = await store2.getCwd("conv1");
+		expect(result).toBe("/persisted/path");
+	});
+
+	it("cwd of one conversation does not leak into another", async () => {
+		const store = createConversationStore(storage);
+		await store.setCwd("convA", "/path/a");
+		await store.setCwd("convB", "/path/b");
+		expect(await store.getCwd("convA")).toBe("/path/a");
+		expect(await store.getCwd("convB")).toBe("/path/b");
+	});
+});
diff --git a/packages/conversation-store/src/store.ts b/packages/conversation-store/src/store.ts
index 6b91d58..0948f64 100644
--- a/packages/conversation-store/src/store.ts
+++ b/packages/conversation-store/src/store.ts
@@ -11,6 +11,7 @@ import { defineService } from "@dispatch/kernel";
 import {
 	chunkKey,
 	chunkPrefix,
+	cwdKey,
 	metricsKey,
 	metricsPrefix,
 	metricsSeqKey,
@@ -28,6 +29,10 @@ export interface ConversationStore {
 	) => Promise<readonly StoredChunk[]>;
 	readonly appendMetrics: (conversationId: string, metrics: TurnMetrics) => Promise<void>;
 	readonly loadMetrics: (conversationId: string) => Promise<readonly TurnMetrics[]>;
+	/** The persisted working directory for a conversation, or null if never set. */
+	readonly getCwd: (conversationId: string) => Promise<string | null>;
+	/** Persist (upsert) the working directory for a conversation. */
+	readonly setCwd: (conversationId: string, cwd: string) => Promise<void>;
 }
 
 export const conversationStoreHandle = defineService<ConversationStore>("conversation-store/store");
@@ -154,5 +159,16 @@ export function createConversationStore(
 
 			return result;
 		},
+
+		async getCwd(conversationId) {
+			return await storage.get(cwdKey(conversationId));
+		},
+
+		async setCwd(conversationId, cwd) {
+			await storage.set(cwdKey(conversationId), cwd);
+			if (logger !== undefined) {
+				logger.debug("cwd set", { conversationId });
+			}
+		},
 	};
 }