Wireless keyboard and wireless mouse works till login screen and stop working post login.

Dear Experts,

I am using macmini (apple silicon) with wireless keyboard & mouse from logitech. I mistekenly disabled the bluetooth from my user login and now facing challenges to turn it back on.

Both wireless keyboard and mouse work fine over bluetooth till the login screen where password is prompted. after entering password using keyboard, both the input devices stop working may be because bluetooth is still disabled. I do not have a apple compatible USB keyboard to connect through cable. however my mouse is connected through USB cable but that works neither over USB or bluetooth interface.

I tried entering into recovery mode and setting up the ControllerPowerState to "1" in "com.apple.Bluetooth" using command line but that doesn't work for me, after login screen both the devices stop working. OS version is 15.5.

Please share your thoughs and experiences on how can I recover & enable the bluetooth again?