I am also really interested in getting bluetooth working reliably on the pyra. I use xubuntu (debian based and uses pulse) and bought a cheap stereo headset to test stuff. Connecting was a little bit tricky but worked. I never got the headset part working (i lost interest and stoped trying).
My plan was to by something like this (
https://www.amazon.com/dp/B0154G9CYY) (there are probably cheaper clones) and use my favorite headphone with it.
(This thing is relay neat it can also be used without any headphones connected so you are always ready to answer the
phone pyra.)
But I really want to now, if it will ever be possible to use some setup like this reliably, including reconnecting on wakeup trigged by a phone call, or even keeping the connection in standby and showing the caller id.
I don't have high hopes this will ever work out of the box like on most "smart" phones, but who knows.
(as a funny side note: while writing this my audio got messed up (static noise) time to restart pulse

"pulseaudio -k;pkill xfce4-volumed;pulseaudio --start;xfce4-volumed&")