How to transfer a bluetooth headset microphone from Debian 11 to Home Assistant Rhasspy Assistant?

Did you look at this Select default audio device - #5 by arminJacobson , it look like HA need to assign the default input or it will not work, you probably need to change the profile of the sound device

" How to change the profile of a sound device

Thanks to this page from the Arch wiki, I was able to change the profile using pactl. The syntax is as follows:
pactl set-card-profile <symbolic-name> <profilename>