Setting default profile for bluetooth headphones with pipewire

I have BOSE bluetooth headphones successfully connected and paired. I am using pipewire instead of pulseaudio, as was recommended to me here:

There are two main profiles:
High Fidelity (A2DP sink)
Headset (HSP/HPF)

And they both work. AFAIK pipewire has not yet implemented automatic switching of profiles according to context, so I am interested in the next best thing, which is defining a default profile.
Right now, it defaults to “A2DP sink” but I would like to change it to “Headset”.

EDIT: It is now supposed to switch profiles automatically (although I don’t see that happening)

“- Bluetooth can now automatically switch between headset
and audio profile.”