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/lib/socket.ts

@@ -1,14 +1,20 @@
-import { io, type Socket } from 'socket.io-client';
+import { io } from 'socket.io-client';
+import type { ChatSocket } from './chat-contract';
 
-let socket: Socket | null = null;
+let socket: ChatSocket | null = null;
 
-export function getSocket(): Socket {
+export function getSocket(): ChatSocket {
   if (!socket) {
+    // socket.io-client 4.8.3's `io()` factory declaration always returns the
+    // default unparameterized Socket (it accepts no <ListenEvents, EmitEvents>
+    // generics), so this one cast is the unavoidable boundary between that and the
+    // typed `/chat` contract. Every other call site uses the resulting ChatSocket
+    // with no further assertions.
     socket = io('/chat', {
       withCredentials: true,
       autoConnect: false,
       transports: ['websocket', 'polling'],
-    });
+    }) as unknown as ChatSocket;
 
     // Reset singleton reference when socket is fully closed so the next
     // getSocket() call creates a fresh instance instead of returning a