Mouse and keyboard with bluetooth not working on login when activating FileVault

I was using my MX Keys keyboard and MX Master 3 mouse over bluetooth on my iMac 2019, with macOS 12.4.

This macOS install is actually cumulative upgrades since the release of Monterey, not a clean install.

For security, I decided to enable FileVault, but after that, during login they don't work anymore.

I read that macOS 12.4 solved this problem, but it still persists, even removing and re-pairing both.

How can I fix this problem? Using the Logitech Unify dongle causes a lot of lag.