Same problema here, since upgrade to 12.3 all my BT devices are randomly disconecting, interference with headsets, even using magic key board, amgic maouse and airpods pro. But tried with logitech MxMaster 3 mouse an Mx Master keyboard it's the same problem, and that hasn't happend before upgrading 12.3. Apple, please do something

After installing 12.3.1 that supposedly corrects bluetooth problems, i'm still having same issues. Logitech MX Master 3 and MX Keys, keeps disconnecting randomly, Magic Keyboard and magic mouse improved but if you connect any additional BT device (like airpods pro) it stats lagging a lot. Studio 3, didn't work at all, sony's WM..M4 works now, but i hace to switch off keyboard and mouse. Tried to kill bluetoothHD, delete PLIST file, reset SMC.. but still the same. This weekend going back to BigSur, hope this will be corrected in the future.