Fix Android/iOS VoIP Calling Notification & Routing Issue (Flutter + Firebase)

We have a mobile app built in Flutter (Android & iOS). The app includes VoIP-style calling using Firebase and flutter_callkit_incoming.

The core logic is working, but there are issues:
Incoming call doesn’t show properly on the lock screen.
Tapping Accept sometimes opens the home screen instead of the call screen.
The caller hears ringing, but the callee sees a missed call.
Notifications are delayed or misrouted.

We need a Flutter expert to:
Fix call intent routing and screen behavior for VoIP (Android & iOS)
Ensure full call screen appears even in background/locked state
Handle FirebaseMessaging (onMessage, onMessageOpenedApp, getInitialMessage)
Debug/test FCM payload behavior

Backend: Firebase + AWS Lambda (Python)
Target platform: Flutter mobile (Android & iOS)

We’ll provide:
Firebase credentials
AWS Lambda access (if needed)
Full GitHub repo (frontend + backend)

Budget: $200 USD fixed
Deadline: 7 days MAX
Only the VoIP fix is in scope — no unrelated app features should be touched.