If you want to turn off Bluetooth automatically when you close the MacBook lid, install the FluTooth utility.
macOS 12.2 users have been suffering from rapid battery drain when Bluetooth is on for some time. And although at the time of reading this post, the problem is no longer relevant, but its solution can be useful in everyday life.
If you suffer from the bug described above, or just want to turn off Bluetooth automatically when you close the MacBook lid, install the FluTooth utility.
The only setting available in it is Run at startup. If FluTooth is running, then Bluetooth will automatically turn off and on. So simple.