Detect car in background (Via bluetooth, MotionActivity or other ?)

If only you supported CarPlay...

You can use AVFoundation

do {
      try audioSession.setCategory(AVAudioSessionCategoryPlayAndRecord, with: [.allowBluetooth, .allowBluetoothA2DP, .allowAirPlay
      try audioSession.setActive(true)
} catch {
     fatalError("Audio session failure")
}

and add an observer

NotificationCenter.default.addObserver(self,
                                               selector: #selector(handleRouteChange),
                                               name: .AVAudioSessionRouteChange,
                                               object: AVAudioSession.sharedInstance())

@objc func handleRouteChange(_ notification: Notification) {
        guard let userInfo = notification.userInfo,
            let reasonValue = userInfo[AVAudioSessionRouteChangeReasonKey] as? UInt,
            let reason = AVAudioSessionRouteChangeReason(rawValue:reasonValue) else {
                return
        }
        switch reason {
        case .newDeviceAvailable:
            print("Handle new device available.")
            let session = AVAudioSession.sharedInstance()
            for output in session.currentRoute.outputs where output.portType == AVAudioSessionPortHeadphones {
            }
        case .oldDeviceUnavailable:
            print("Handle old device removed.")
            if let previousRoute =
                userInfo[AVAudioSessionRouteChangePreviousRouteKey] as? AVAudioSessionRouteDescription {
                for output in previousRoute.outputs where output.portType == AVAudioSessionPortHeadphones {
                }
            }
        default: ()
        }
     }