Hi @flavonol,
I think this is a bug introduced in Fedora 35. Audio output was switching automatically in F34. I have reported the bug here but there is no response yet.
My problem is that when I plug the HDMI cable, the Output Device does not switch automatically. The worse part is that if I unplug it I loose sound on my laptop and have to select the builtin speakers manually every time. You can see more detailed explanation here.
Can you confirm you have the same problem if you unplug your HDMI?