sidecar self-registration: sidecars connect to API server instead of vice versa

Flips the connection model so sidecars register themselves with the API
server via WebSocket at /api/sidecar/register, enabling dynamic discovery,
location independence, and automatic reconnection from either side.

- Add registration protocol types and PTY command/event types
- Create sidecar-registry.ts (replaces sidecar-client.ts) as passive registry
- Create sidecar connector (connect.ts) with exponential backoff reconnect
- Convert process sidecar from WS server to WS client
- Convert PTY sidecar from WS server to multiplexed WS client
- Simplify terminal bridge to thin adapter using registry
- Add PTY sidecar as PM2-managed process
- Update all consumer imports

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/servers/channels/send-claude-code.ts

@@ -1,6 +1,6 @@
 import { logger } from '@@/api/pi/logger';
 import type { MessageCost, PiEvent } from '@@/api/pi/types';
-import * as sidecar from '@@/sidecar-client';
+import * as sidecar from '@@/sidecar-registry';
 
 type ClaudeCodeParams = {
   userId: number;