@zipb
I don't use BT with my Designare Z390 which has the Fenvi FV-T919 card installed. But to see if my hack also had problems with BT, I just checked both Monterey and the latest Ventura public beta to see if my iPhone SE with current iOS would connect via BT. It would pair and for a second or two show "Connected," then immediately disconnect.
If I repeatedly retry to "Connect" the iPhone, it would show "Connected," but instantaneously disconnect.
So I confirm your BT problem with the Designare. I also tried BT with my Z690 Aero G which has a Broadcom BCM94360NG Key A/E M.2 WiFi/BT module replacing the Intel WiFi module and it exhibits the same problem with Big Sur, Monterey, and public beta 3 Ventura. Maybe my iPhone model is a factor.
Since I don't use BT, I don't have time at this point to work the issue.