When switching to tty, bluetooth headset is being disconnected

I have a bluetooth headset connected to my computer. Whenever I switch to a different tty, it disconnects and as a result, the audio playback stops. I want this behaviour to change. How do I do that?

Steps:

  1. in GNOME/Wayland session, have a bluetooth headset connected
  2. start any audio playback (e.g. opening a .mp3 file using totem a.k.a. Videos)
  3. switch to a different tty, e.g. [Ctrl]+[Alt]+[F3]
  4. try to listen to audio

What happens:
My headset says “bluetooth disconnected”. Audio playback stops.

What do I expect to happen:
My headset should stay connected. Audio playback should continue.