feat: integrate Firebase Cloud Messaging for push notifications

[GRACENOBLE]

Summary

Add Firebase Cloud Messaging (FCM) to deliver push notifications to Android and web clients from the Go backend.

Scope

Backend (Go)

• Add firebase.google.com/go/v4 Admin SDK (shared with the Firebase Auth integration from feat: add Firebase Authentication across all app layers #15)
• Add a notification service in usecase/ with a SendNotification interface
• Implement in infrastructure/ using the FCM HTTP v1 API via the Admin SDK
• Expose an internal helper that other use cases can call to trigger notifications (e.g. after a background job completes via QStash feat: integrate Asynq + Redis Streams for background jobs and event-driven messaging #18)
• Store FIREBASE_SERVICE_ACCOUNT_JSON (or path to the key file) in env — document in backend/.env.example

Web (Next.js)

• Add firebase JS SDK (shared with Firebase Auth feat: add Firebase Authentication across all app layers #15)
• Request notification permission and obtain an FCM registration token on the client
• Register a service worker (public/firebase-messaging-sw.js) to handle background messages
• Send the registration token to the backend so it can be stored per-user
• Handle foreground messages via onMessage()

Mobile (Android / Jetpack Compose)

• Add com.google.firebase:firebase-messaging via version catalog
• Extend FirebaseMessagingService to handle foreground and background messages
• On token refresh, send the new FCM token to the backend
• Display notifications using NotificationCompat for background delivery; handle foreground in-app

Backend storage

• Migration: add fcm_tokens table (user_id, token, platform, created_at) so the backend can fan-out to all of a user's devices

Acceptance criteria

• Backend can send a notification to a specific FCM token via the Admin SDK
• Web client receives foreground and background push notifications
• Android client receives foreground and background push notifications
• FCM tokens are stored per-user and cleaned up on logout (ties into feat: add Firebase Authentication across all app layers #15)
• FIREBASE_SERVICE_ACCOUNT_JSON added to backend/.env.example with a placeholder and comment
• Migration created for fcm_tokens table
• Tests written for the notification use case (unit) and token storage (integration)
• Docs added to backend/docs/fcm.md, web/docs/fcm.md, and mobile/docs/fcm.md

Dependencies

• feat: add Firebase Authentication across all app layers #15 Firebase Auth (shares Firebase project and Admin SDK setup)