chat: rename the pi chat transport + model list to chat (Stage 4b/1)

Pure rename, no behavior change. Moves the misnamed "pi" chat harness into the
chat namespace:

- api/pi/{websocket,session-manager,types,logger,list-models} → api/chat/
- merge api/pi/rest.ts into api/chat/chat.ts (/pi/models → /chat/models,
  /pi/stt → /chat/stt); drop the piRestRouter mount
- PiEvent → ChatEvent, piWebsocket → chatWebsocket, listPiModels → listChatModels
- WS route /api/pi/chat/ws → /api/chat/ws, provider tag 'pi' → 'chat'
- frontend: useChat/useAudioRecording URLs, usePiModels→useModels /
  useVisiblePiModels→useVisibleModels / useEnabledPiModels→useEnabledModels,
  'PI_MODELS' query key → 'CHAT_MODELS', attachments provider 'pi-mono' → 'chat'

The /pi-mono provider/harness settings router is renamed separately (next commit).
Note: the WS route change requires the mobile app to point at /api/chat/ws.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/servers/sidecar-registry.ts

@@ -14,7 +14,7 @@ import type {
   VncSessionInfo,
 } from './sidecar/protocol';
 import type { SidecarRegistration } from './sidecar/registration-protocol';
-import type { PiEvent } from './api/pi/types';
+import type { ChatEvent } from './api/chat/types';
 
 // ── Types ──
 
@@ -339,7 +339,7 @@ export function clearClaudeSession(sessionKey: string, email?: string): void {
   }
 }
 
-export function onClaudeEvent(handler: (sessionKey: string, event: PiEvent) => void): () => void {
+export function onClaudeEvent(handler: (sessionKey: string, event: ChatEvent) => void): () => void {
   return on('claude:event', (msg) => {
     if (msg.type === 'claude:event') {
       handler(