feat: add session creation and ID management with localStorage

- Session store with UUID v4 generation and localStorage persistence
- Session ID in URL params (?session=<id>) for deep linking
- "New Chat" button for creating fresh sessions
- Message history persisted per session
- Session title auto-generated from first user message

Closes #11

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/routes/chat/+page.svelte

@@ -1,4 +1,7 @@
 <script lang="ts">
+	import { page } from '$app/stores';
+	import { goto } from '$app/navigation';
+	import { resolveRoute } from '$app/paths';
 	import type { ChatMessage } from '$lib/types';
 	import type { SubagentResult } from '$lib/proto/llm_multiverse/v1/common_pb';
 	import MessageList from '$lib/components/MessageList.svelte';
@@ -8,21 +11,45 @@
 	import FinalResult from '$lib/components/FinalResult.svelte';
 	import { processRequest, OrchestratorError } from '$lib/services/orchestrator';
 	import { OrchestrationState } from '$lib/proto/llm_multiverse/v1/orchestrator_pb';
+	import { sessionStore } from '$lib/stores/sessions.svelte';
 
 	let messages: ChatMessage[] = $state([]);
 	let isStreaming = $state(false);
 	let error: string | null = $state(null);
-	let sessionId = $state(crypto.randomUUID());
 	let orchestrationState: OrchestrationState = $state(OrchestrationState.UNSPECIFIED);
 	let intermediateResult: string = $state('');
 	let finalResult: SubagentResult | null = $state(null);
 
+	// Initialize session from URL or create new one
+	$effect(() => {
+		const sessionParam = $page.url.searchParams.get('session');
+		const session = sessionStore.getOrCreateSession(sessionParam ?? undefined);
+		messages = [...session.messages];
+		if (!sessionParam || sessionParam !== session.id) {
+			const url = `${resolveRoute('/chat')}?session=${session.id}`;
+			// eslint-disable-next-line svelte/no-navigation-without-resolve
+			goto(url, { replaceState: true });
+		}
+	});
+
+	function handleNewChat() {
+		const session = sessionStore.createSession();
+		messages = [];
+		error = null;
+		finalResult = null;
+		const url = `${resolveRoute('/chat')}?session=${session.id}`;
+		// eslint-disable-next-line svelte/no-navigation-without-resolve
+		goto(url);
+	}
+
 	async function handleSend(content: string) {
 		error = null;
 		orchestrationState = OrchestrationState.UNSPECIFIED;
 		intermediateResult = '';
 		finalResult = null;
 
+		const sessionId = sessionStore.activeSessionId!;
+
 		const userMessage: ChatMessage = {
 			id: crypto.randomUUID(),
 			role: 'user',
@@ -39,6 +66,7 @@
 		};
 		messages.push(assistantMessage);
 
+		sessionStore.updateMessages(sessionId, messages);
 		isStreaming = true;
 
 		try {
@@ -69,13 +97,21 @@
 			};
 		} finally {
 			isStreaming = false;
+			sessionStore.updateMessages(sessionId, messages);
 		}
 	}
 </script>
 
 <div class="flex h-screen flex-col">
-	<header class="border-b border-gray-200 bg-white px-4 py-3">
+	<header class="flex items-center justify-between border-b border-gray-200 bg-white px-4 py-3">
 		<h1 class="text-lg font-semibold text-gray-900">Chat</h1>
+		<button
+			type="button"
+			onclick={handleNewChat}
+			class="rounded-lg bg-gray-100 px-3 py-1.5 text-sm font-medium text-gray-700 hover:bg-gray-200"
+		>
+			New Chat
+		</button>
 	</header>
 
 	<MessageList {messages} />