feat(web): add typed SPA chat

Bring the chat experience into the Vite/React-Router SPA on the exact typed
Socket.IO /chat contract from @mosaicstack/types, replacing the /chat
placeholder behind AuthGuard. Surfaces message:ack (with an accessible
status), agent:start, streamed agent:text/agent:thinking, tool start/end
status, agent:end with usage, session:info (thinking controls + routing
decision), commands:manifest, command:result, command:approval (with a
one-time approved-run affordance), system:reload (refreshing the rendered
manifest), and error, and emits message/abort/set:thinking/command:execute/
command:approve with exact payloads.

The gateway does not guarantee message:ack is the first event for a new
conversation (session:info, and error on auth/session-creation failure, can
both arrive first) — conversation-scoped events now adopt the conversation
from whichever scoped event names it first while a send is pending, then
filter everything else against that established conversation. A typed error
stops streaming instead of leaving Stop stuck active; agent:end no longer
appends an empty assistant turn when there is no text or thinking; and a
second message can no longer be sent while a turn is streaming.

Command approval is now integrity-checked end to end: only one
command:approve request may be outstanding at a time (a concurrent request
is ignored rather than overwriting the pending command/args), a stale or
mismatched command:approval response cannot replace active approval state,
and running an approved command clears its approval state immediately (via
a ref, before React re-renders) so a double-click cannot replay
command:execute.

The `/chat` socket is now typed at a single boundary: apps/web/src/lib/
socket.ts narrows socket.io-client's untyped `io()` return value to
`ChatSocket` (Socket<ServerToClientEvents, ClientToServerEvents>) once, at
creation, via the one assertion the library's types force; every consumer
(use-chat-connection.ts) then gets fully checked `on`/`emit` calls with no
further casts. The shared contract types live in the new
apps/web/src/lib/chat-contract.ts (replacing the old spa/chat/types.ts
shim), which re-exports them via type-only imports resolved directly
against packages/types/src (apps/web has no @mosaicstack/types package
dependency, so this stays source-only and is erased at compile time —
no package manifest or lockfile is touched). The two recorded-event test
suites now drive a shared, typed fake socket
(spa/chat/test-support/fake-chat-socket.ts) instead of an untyped
`(event: string, payload: unknown)` harness, so a wrong event name or
malformed payload fails to compile.

apps/web/src/spa/chat/test-support/fake-chat-socket.ts

@@ -0,0 +1,77 @@
+import { vi } from 'vitest';
+import type { ClientToServerEvents, ServerToClientEvents } from '@/lib/chat-contract';
+
+type ServerEvent = keyof ServerToClientEvents;
+type ClientEvent = keyof ClientToServerEvents;
+type ServerHandler<K extends ServerEvent> = ServerToClientEvents[K];
+type ClientPayload<K extends ClientEvent> = Parameters<ClientToServerEvents[K]>[0];
+
+export interface EmittedEvent<K extends ClientEvent = ClientEvent> {
+  event: K;
+  payload: ClientPayload<K>;
+}
+
+/** The subset of a Socket.IO `ChatSocket` that `useChatConnection` drives. */
+export interface FakeChatSocket {
+  connected: boolean;
+  connect(): FakeChatSocket;
+  on<K extends ServerEvent>(event: K, handler: ServerHandler<K>): FakeChatSocket;
+  off<K extends ServerEvent>(event: K, handler: ServerHandler<K>): FakeChatSocket;
+  emit<K extends ClientEvent>(event: K, payload: ClientPayload<K>): FakeChatSocket;
+}
+
+/**
+ * A typed in-memory stand-in for `getSocket()`. Unlike a bare
+ * `(event: string, payload: unknown) => void` mock, every public method here is
+ * checked against the real `/chat` contract — a typo'd event name or a payload
+ * missing a required field fails to compile instead of silently no-op'ing at
+ * runtime.
+ */
+export function createFakeChatSocket(): {
+  socket: FakeChatSocket;
+  listeners: Map<ServerEvent, Set<(payload: never) => void>>;
+  emitted: EmittedEvent[];
+  serverEmit<K extends ServerEvent>(
+    event: K,
+    payload: Parameters<ServerToClientEvents[K]>[0],
+  ): void;
+} {
+  const listeners = new Map<ServerEvent, Set<(payload: never) => void>>();
+  const emitted: EmittedEvent[] = [];
+
+  // Internal storage is intentionally keyed loosely (the per-event handler shape
+  // varies by K, which a single Map can't express); the generic signatures on the
+  // exported `socket`/`serverEmit` above and below are what keep test call sites
+  // type-checked against ServerToClientEvents/ClientToServerEvents.
+  const socket = {
+    connected: false,
+    connect: vi.fn(function connect(this: void) {
+      socket.connected = true;
+      return socket;
+    }),
+    on: vi.fn(function on(this: void, event: ServerEvent, handler: (payload: never) => void) {
+      if (!listeners.has(event)) listeners.set(event, new Set());
+      listeners.get(event)?.add(handler);
+      return socket;
+    }),
+    off: vi.fn(function off(this: void, event: ServerEvent, handler: (payload: never) => void) {
+      listeners.get(event)?.delete(handler);
+      return socket;
+    }),
+    emit: vi.fn(function emit(this: void, event: ClientEvent, payload: unknown) {
+      emitted.push({ event, payload } as EmittedEvent);
+      return socket;
+    }),
+  } as unknown as FakeChatSocket;
+
+  function serverEmit<K extends ServerEvent>(
+    event: K,
+    payload: Parameters<ServerToClientEvents[K]>[0],
+  ): void {
+    for (const handler of listeners.get(event) ?? []) {
+      (handler as (payload: Parameters<ServerToClientEvents[K]>[0]) => void)(payload);
+    }
+  }
+
+  return { socket, listeners, emitted, serverEmit };
+}