feat(03-04): wire startOutboxWorker into index.ts at boot

- Import startOutboxWorker beside startBrokerPoller import
- Call startOutboxWorker() immediately after startBrokerPoller()
- Worker drains D-05 outbox every 15s alongside the 5-min ctag poller

apps/api/src/index.ts

@@ -8,6 +8,7 @@ import { sseRouter } from './routes/sse.js'
 import { oidcAuthMiddleware, processOAuthCallback } from './auth/middleware.js'
 import { devAuthBypass } from './auth/devBypass.js'
 import { startBrokerPoller } from './broker/poller.js'
+import { startOutboxWorker } from './broker/outboxWorker.js'
 
 export const app = new Hono()
 
@@ -52,6 +53,8 @@ app.route('/api/sse', sseRouter)
 // Start the CalDAV broker poller (5-min cron, D-13 ctag change-detection)
 // Runs in the background — errors are caught and logged per-credential (T-03-04)
 startBrokerPoller()
+// Drain the D-05 outbox every 15s: dispatches pending CalDAV writes to Fastmail
+startOutboxWorker()
 
 // Serve React PWA static assets from ./public (Vite build output)
 app.use('/assets/*', serveStatic({ root: './public' }))