pulseaudio – Issue switching bluetooth headphones from Windows 11 to Ubuntu 24.04

Every time I connect my bluetooth headphones to Windows 11 I am not able to use them on Ubuntu 24.04 unless I “forget” the device from Windows first.

Without removing the headphones from Windows first, I tried the following commands in Ubuntu:

bluetoothctl disconnect 
bluetoothctl untrust 
bluetoothctl remove 
bluetoothctl connect 
bluetoothctl trust 

In this case I get the headphones connected but PulseAudio won’t recognise them as output device. So at the moment the only way left to use bluetooth headphones previously connected to Windows, it is “forgetting” them first from Windows. Vice versa is not true tho, as Windows will be able to use them, even if previously connected to Ubuntu (same for other Android devices).

Is there a way to get the same Windows’ behaviour with Ubuntu?