Definitely have the same problem. Mine was already before the latest update but since 12.3 it is really bad. Indeed, disconnecting and reconnecting all the time. Lagging when listening to music, YouTube videos are impossible to watch because you miss half of the words spoken. Also have Wi-Fi problems where my MacBook just loses the Wi-Fi connection and doesn't seem to know how to reconnect. After restarting the router, the Wi-Fi connection miraculously works again for a while.
Bluetooth though is really annoying (beyond irritation) and it somehow seems that over the last months or even years Apple and their products lose their impeccable image of having no meaningful problems.