Problem with Bluetooth headsets, iPhone and Apple Watch

Hardware and Accessories

I have two pairs of Bluetooth headphones. BeatsX and Plantronic Voyager Edge.
Plantronic is connected simultaneously to the iPhone and Apple Watch.
The sound switching works well depending on which device is sending, for example, VoiceOver speech.

The problem occurs when I want to play some media, for example an audiobook in or Podcast.
I tap the play button and the track is played for 1 second, then it stops.
If I disconnect the handset from Apple Watch, the problem disappears.
I do not have a problem with BeatsX. Because they can not choose to play the sound from the currently playing device.

Have you met with such a problem, and more importantly if there is any way that it would work properly.