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/claude-manager.ts

@@ -1,6 +1,6 @@
 import { join } from 'node:path';
 import type { Subprocess } from 'bun';
-import type { PiEvent } from '../../api/pi/types';
+import type { ChatEvent } from '../../api/chat/types';
 import type { ClaudeSpawnParams, ClaudeSpawnStreamingParams, ClaudeCodeResult } from '../protocol';
 import { buildSandboxPrefix, buildRunuserSuffix, SANDBOX_HOME } from '../sandbox';
 import { setClaudeSession, clearClaudeSession, getClaudeSession } from './state';
@@ -145,7 +145,7 @@ export async function spawnClaude(params: ClaudeSpawnParams): Promise<ClaudeCode
 
 export async function spawnClaudeStreaming(
   params: ClaudeSpawnStreamingParams,
-  onEvent: (event: PiEvent) => void,
+  onEvent: (event: ChatEvent) => void,
 ): Promise<void> {
   const { prompt, sessionKey, email } = params;