feat: PWA push notifications — service worker, VAPID, subscription management

- Add web-push VAPID backend with push_subscriptions table (migration 078)
- Backend push module with sendPushToUser/sendPushToRoom helpers
- Push routes: GET vapid-key, POST subscribe, DELETE unsubscribe
- Trigger push on new chat messages in direct/group rooms
- PWA manifest, service worker, and icons (72–512px)
- Frontend push lib: SW registration, subscribe/unsubscribe helpers
- Push API in api.ts, SW registered in main.tsx
- usePushSubscription hook for auto-subscribe on permission grant
- PushPermissionRow component in ChatWidget settings view

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

backend/src/app.ts

@@ -34,6 +34,7 @@ import notificationsRoutes from './routes/notifications'
 import scheduleRoutes      from './routes/schedule'
 import loyaltyRoutes       from './routes/loyalty'
 import chatRoutes          from './routes/chat'
+import pushRoutes          from './routes/push'
 import workstationRoutes   from './routes/workstations'
 import agentReleaseRoutes  from './routes/agent-release'
 import wifiSettingsRoutes, { wifiAuthVerify } from './routes/wifi-settings'
@@ -48,6 +49,7 @@ import publicWidgetRoutes from './routes/publicWidget'
 import yookassaWebhookRoutes from './routes/yookassaWebhook'
 import { setupAgentWsRoute } from './agent-ws'
 import { startJobs } from './jobs'
+import { initWebPush } from './push'
 
 export async function buildApp() {
   const fastify = Fastify({
@@ -131,6 +133,7 @@ export async function buildApp() {
   await fastify.register(scheduleRoutes)
   await fastify.register(loyaltyRoutes)
   await fastify.register(chatRoutes)
+  await fastify.register(pushRoutes)
   await fastify.register(workstationRoutes)
   await fastify.register(agentReleaseRoutes)
   await fastify.register(wifiSettingsRoutes)
@@ -147,6 +150,7 @@ export async function buildApp() {
   await fastify.register(setupAgentWsRoute)
 
   startJobs()
+  initWebPush()
 
   return fastify
 }