feat(web): chat UI with conversations and WebSocket streaming (#84)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

apps/web/src/lib/socket.ts

@@ -0,0 +1,15 @@
+import { io, type Socket } from 'socket.io-client';
+
+const GATEWAY_URL = process.env['NEXT_PUBLIC_GATEWAY_URL'] ?? 'http://localhost:4000';
+
+let socket: Socket | null = null;
+
+export function getSocket(): Socket {
+  if (!socket) {
+    socket = io(`${GATEWAY_URL}/chat`, {
+      withCredentials: true,
+      autoConnect: false,
+    });
+  }
+  return socket;
+}

apps/web/src/lib/types.ts

@@ -0,0 +1,19 @@
+/** Conversation returned by the gateway API. */
+export interface Conversation {
+  id: string;
+  userId: string;
+  title: string | null;
+  projectId: string | null;
+  createdAt: string;
+  updatedAt: string;
+}
+
+/** Message within a conversation. */
+export interface Message {
+  id: string;
+  conversationId: string;
+  role: 'user' | 'assistant' | 'system';
+  content: string;
+  metadata?: Record<string, unknown>;
+  createdAt: string;
+}