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/claude/stream-parser.test.ts

@@ -1,10 +1,10 @@
 import { describe, test, expect } from 'bun:test';
 import { processLine, createParseState, parseStream } from './stream-parser';
-import type { PiEvent } from '../../api/pi/types';
+import type { ChatEvent } from '../../api/chat/types';
 import type { StreamParserCallbacks, ParseState } from './stream-parser';
 
-function makeCallbacks(): { events: PiEvent[]; sessionIds: string[]; callbacks: StreamParserCallbacks } {
-  const events: PiEvent[] = [];
+function makeCallbacks(): { events: ChatEvent[]; sessionIds: string[]; callbacks: StreamParserCallbacks } {
+  const events: ChatEvent[] = [];
   const sessionIds: string[] = [];
   return {
     events,