Restart.restartApp() uses a platform channel and must run on the main isolate. Calling it from a background isolate throws: 
Bad state: The BackgroundIsolateBinaryMessenger.instance value is invalid
until BackgroundIsolateBinaryMessenger.ensureInitialized is executed.
Send a message from the background isolate to the main isolate instead. 
// Main isolate: listen for restart signals.
final receivePort = ReceivePort();
receivePort.listen((message) {
  if (message == 'restart') {
    Restart.restartApp();
  }
});

// Spawn the isolate with the SendPort.
await Isolate.spawn(myIsolateFunction, receivePort.sendPort);

// Background isolate: signal instead of calling restartApp() directly.
void myIsolateFunction(SendPort sendPort) {
  // ... your background work ...
  sendPort.send('restart');
}