External bluetooth keyboard and mouse not detected at login screen after reboot

I have a Macbook Pro 15 2018 and Logitech Mx Keys and Mx Master 3 (bluetooth keyboard and mouse) and they are working great.

However when I reboot my mac and get to login screen they are not detected/connected.

When I open the lid and login using the built in keyboard they start working again.

I've found that this my be linked to FileVault and yes I am using FileVault.

My question:

Is there any way to prevent this from happening without turning FileVault off ?

When I put mac to sleep they still keep working and I can wake my mac by pressing a key on the keyboard.

It is linked to FileVault in that Bluetooth pairings are stored per user, not per machine. So until you login (and thus unlock your account) the machine cannot re-pair to your devices. Keyboard backlight settings are also stored per user for some reason, so no backlight until you login. Since sleep doesn't log you out, everything still works.

A related issue is that Bluetooth keyboards also don't work during boot up (never did for me). So if you ever need to go into recovery mode, you need a USB keyboard if the internal one breaks. I don't know how the Apple wireless keyboard bypasses all this, but I assume they cheat and use an unofficial extension to Bluetooth.

If you pair to the Logitech dongle, it will all work as it is essentially a "USB" device. If opening the lid every time is annoying, your only recourse seems to pair to the dongle as well as Bluetooth and plug in the dongle to login (and switching the 1/2/3 selector) which sounds almost as bad.

Hope any of this helped.