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/api/email/accounts.ts

@@ -9,7 +9,7 @@ import {
   updateEmailAccountStatus,
 } from 'officerdb';
 import { validateImapConnection } from './imap-validate';
-import * as sidecar from '../../sidecar-client';
+import * as sidecar from '../../sidecar-registry';
 
 type CreateAccountBody = {
   provider: string;
@@ -137,7 +137,12 @@ accountsRouter.post('/:id/sync', async (ctx) => {
   if (account.status === 'syncing') throw BAD_REQUEST('Account is already syncing');
 
   // Resolve auth before enqueueing
-  const authResult = await resolveAuth(user.id, account.authType, account.email, account.credentials as Record<string, unknown>);
+  const authResult = await resolveAuth(
+    user.id,
+    account.authType,
+    account.email,
+    account.credentials as Record<string, unknown>,
+  );
   if (!authResult.ok) throw BAD_REQUEST(authResult.error);
 
   // Set status immediately so the UI reflects the queued state