Bluetooth keyboard doesn't work during initial boot
I have a MAC mini (M1, 2020, 16GB, 512GB) on Mac OS "Big Sur 11.6".
I have Logitech "MX keys for MAC" Bluetooth keyboard and "MX master 3 for MAC" Bluetooth mouse. I have paired them successfully and they are working well.
However, if I restart my Mac Mini, the Bluetooth keyboard and mouse are not accessible during the initial boot screen (where the system prompts for the password). I need to use a wired USB keyboard to provide the password. After this, the system boots normally, and the Bluetooth keyboard and mouse are auto-detected and start working normally.
How do I fix this problem so that the Bluetooth keyboard and mouse are available during the initial system boot phase?
Mac mini, macOS 11.6