feat(tabs): extract TabBar component with horizontal scroll + sticky end '+'

Move inline tab-bar markup from the composition root into a thin
presentational TabBar in the tabs feature (feature-as-a-library: pure
reducer -> reactive store -> UI). Adds overflow-x scroll (min-w-max strip)
and a sticky right-pinned new-chat '+' that floats over scrolling tabs.
Draft-on-select / create-on-send behavior unchanged.

4 files changed, 211 insertions, 34 deletions

diff --git a/src/app/App.svelte b/src/app/App.svelte
index 811dc75..cc9866e 100644
--- a/src/app/App.svelte
+++ b/src/app/App.svelte
@@ -1,6 +1,7 @@
 <script lang="ts">
 	import type { InvokeMessage } from "@dispatch/ui-contract";
 	import { ChatView, Composer, ModelSelector } from "../features/chat";
+	import { TabBar } from "../features/tabs";
 	import { SurfaceView } from "../features/surface-host";
 	import type { AppStore } from "./store.svelte";
 
@@ -42,40 +43,13 @@
 		</div>
 	{/if}
 
-	<div class="flex items-center gap-2 border-b border-base-300 px-4">
-		<div class="tabs tabs-border flex-1">
-			{#each store.tabs as tab (tab.conversationId)}
-				<div
-					class="tab"
-					class:tab-active={tab.conversationId === store.activeConversationId}
-					role="tab"
-					tabindex="0"
-					onclick={() => store.selectTab(tab.conversationId)}
-					onkeydown={(e) => { if (e.key === "Enter") store.selectTab(tab.conversationId); }}
-				>
-					<span class="max-w-[120px] truncate">{tab.title}</span>
-					<button
-						class="btn btn-ghost btn-xs ml-1"
-						aria-label="Close tab"
-						onclick={(e) => {
-							e.stopPropagation();
-							store.closeTab(tab.conversationId);
-						}}
-					>
-						&times;
-					</button>
-				</div>
-			{/each}
-			<button
-				class="tab"
-				class:tab-active={store.activeConversationId === null}
-				onclick={() => store.newDraft()}
-				aria-label="New chat"
-			>
-				+
-			</button>
-		</div>
-	</div>
+	<TabBar
+		tabs={store.tabs}
+		activeConversationId={store.activeConversationId}
+		onSelect={(id) => store.selectTab(id)}
+		onClose={(id) => store.closeTab(id)}
+		onNewDraft={() => store.newDraft()}
+	/>
 
 	<div class="flex flex-1 flex-col overflow-hidden">
 		<div class="flex items-center gap-2 px-4 py-2">
diff --git a/src/features/tabs/index.ts b/src/features/tabs/index.ts
index c01d4ac..835788a 100644
--- a/src/features/tabs/index.ts
+++ b/src/features/tabs/index.ts
@@ -12,3 +12,4 @@ export {
 } from "./tabs";
 export type { TabsStorage, TabsStore } from "./tabs-store.svelte";
 export { createTabsStore } from "./tabs-store.svelte";
+export { default as TabBar } from "./ui/TabBar.svelte";
diff --git a/src/features/tabs/ui.test.ts b/src/features/tabs/ui.test.ts
new file mode 100644
index 0000000..53df0be
--- /dev/null
+++ b/src/features/tabs/ui.test.ts
@@ -0,0 +1,148 @@
+import { render, screen } from "@testing-library/svelte";
+import userEvent from "@testing-library/user-event";
+import { describe, expect, it, vi } from "vitest";
+import type { Tab } from "./tabs";
+import TabBar from "./ui/TabBar.svelte";
+
+const sampleTabs: readonly Tab[] = [
+	{ conversationId: "c1", model: "openai/gpt-4", title: "First" },
+	{ conversationId: "c2", model: "anthropic/claude-3", title: "Second" },
+	{ conversationId: "c3", model: "google/gemini", title: "Third" },
+];
+
+describe("TabBar", () => {
+	it("renders one role=tab element per tab showing each title", () => {
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c1",
+				onSelect: vi.fn(),
+				onClose: vi.fn(),
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const tabs = screen.getAllByRole("tab");
+		expect(tabs).toHaveLength(sampleTabs.length);
+		expect(tabs[0]).toHaveTextContent("First");
+		expect(tabs[1]).toHaveTextContent("Second");
+		expect(tabs[2]).toHaveTextContent("Third");
+	});
+
+	it("applies tab-active to the active tab only", () => {
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c2",
+				onSelect: vi.fn(),
+				onClose: vi.fn(),
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const tabs = screen.getAllByRole("tab");
+		expect(tabs[0]).not.toHaveClass("tab-active");
+		expect(tabs[1]).toHaveClass("tab-active");
+		expect(tabs[2]).not.toHaveClass("tab-active");
+	});
+
+	it("applies tab-active to New chat button when activeConversationId is null", () => {
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: null,
+				onSelect: vi.fn(),
+				onClose: vi.fn(),
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const newChat = screen.getByRole("button", { name: "New chat" });
+		expect(newChat).toHaveClass("tab-active");
+	});
+
+	it("calls onSelect with the conversationId when a tab is clicked", async () => {
+		const onSelect = vi.fn();
+		const onClose = vi.fn();
+		const user = userEvent.setup();
+
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c1",
+				onSelect,
+				onClose,
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const tabs = screen.getAllByRole("tab");
+		const secondTab = tabs[1];
+		if (!secondTab) throw new Error("second tab not found");
+		await user.click(secondTab);
+
+		expect(onSelect).toHaveBeenCalledTimes(1);
+		expect(onSelect).toHaveBeenCalledWith("c2");
+		expect(onClose).not.toHaveBeenCalled();
+	});
+
+	it("calls onClose when the close button is clicked and does not call onSelect", async () => {
+		const onSelect = vi.fn();
+		const onClose = vi.fn();
+		const user = userEvent.setup();
+
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c1",
+				onSelect,
+				onClose,
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const closeButtons = screen.getAllByRole("button", { name: "Close tab" });
+		const firstClose = closeButtons[0];
+		if (!firstClose) throw new Error("first close button not found");
+		await user.click(firstClose);
+
+		expect(onClose).toHaveBeenCalledTimes(1);
+		expect(onClose).toHaveBeenCalledWith("c1");
+		expect(onSelect).not.toHaveBeenCalled();
+	});
+
+	it("calls onNewDraft when the New chat button is clicked", async () => {
+		const onNewDraft = vi.fn();
+		const user = userEvent.setup();
+
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c1",
+				onSelect: vi.fn(),
+				onClose: vi.fn(),
+				onNewDraft,
+			},
+		});
+
+		const newChat = screen.getByRole("button", { name: "New chat" });
+		await user.click(newChat);
+
+		expect(onNewDraft).toHaveBeenCalledTimes(1);
+	});
+
+	it("the New chat button has the sticky class", () => {
+		render(TabBar, {
+			props: {
+				tabs: sampleTabs,
+				activeConversationId: "c1",
+				onSelect: vi.fn(),
+				onClose: vi.fn(),
+				onNewDraft: vi.fn(),
+			},
+		});
+
+		const newChat = screen.getByRole("button", { name: "New chat" });
+		expect(newChat).toHaveClass("sticky");
+	});
+});
diff --git a/src/features/tabs/ui/TabBar.svelte b/src/features/tabs/ui/TabBar.svelte
new file mode 100644
index 0000000..76fab05
--- /dev/null
+++ b/src/features/tabs/ui/TabBar.svelte
@@ -0,0 +1,54 @@
+<script lang="ts">
+	import type { Tab } from "../tabs";
+
+	let {
+		tabs,
+		activeConversationId,
+		onSelect,
+		onClose,
+		onNewDraft,
+	}: {
+		tabs: readonly Tab[];
+		activeConversationId: string | null;
+		onSelect: (conversationId: string) => void;
+		onClose: (conversationId: string) => void;
+		onNewDraft: () => void;
+	} = $props();
+</script>
+
+<div class="overflow-x-auto border-b border-base-300">
+	<div class="tabs tabs-border min-w-max">
+		{#each tabs as tab (tab.conversationId)}
+			<div
+				class="tab"
+				class:tab-active={tab.conversationId === activeConversationId}
+				role="tab"
+				tabindex="0"
+				onclick={() => onSelect(tab.conversationId)}
+				onkeydown={(e) => {
+					if (e.key === "Enter") onSelect(tab.conversationId);
+				}}
+			>
+				<span class="max-w-[120px] truncate">{tab.title}</span>
+				<button
+					class="btn btn-ghost btn-xs ml-1"
+					aria-label="Close tab"
+					onclick={(e) => {
+						e.stopPropagation();
+						onClose(tab.conversationId);
+					}}
+				>
+					&times;
+				</button>
+			</div>
+		{/each}
+		<button
+			class="tab sticky right-0 z-10 bg-base-200 shadow-[-2px_0_4px_-1px_rgba(0,0,0,0.2)]"
+			class:tab-active={activeConversationId === null}
+			aria-label="New chat"
+			onclick={() => onNewDraft()}
+		>
+			+
+		</button>
+	</div>
+</div>