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/sidecar/protocol.ts

@@ -113,3 +113,31 @@ export type PiSpawnParams = {
   model: string;
   sessionFile?: string;
 };
+
+// ── PTY types ──
+
+export type PtyInitConfig = {
+  sessionId: string;
+  shell?: { command: string; args?: string[] };
+  cwd?: string;
+  homeDir?: string;
+  userLabel?: string;
+  username?: string;
+  host?: boolean;
+  cols?: number;
+  rows?: number;
+  env?: Record<string, string>;
+};
+
+// PTY commands (API → PTY sidecar)
+export type PtyCommand =
+  | { type: 'pty:init'; id: string; sessionId: string; config: PtyInitConfig }
+  | { type: 'pty:input'; id: string; sessionId: string; data: string }
+  | { type: 'pty:resize'; id: string; sessionId: string; cols: number; rows: number }
+  | { type: 'pty:close'; id: string; sessionId: string };
+
+// PTY events (PTY sidecar → API)
+export type PtyEvent =
+  | { type: 'pty:ready'; id: string; sessionId: string }
+  | { type: 'pty:output'; sessionId: string; data: string }
+  | { type: 'pty:exit'; sessionId: string; exitCode: number; signal?: number };