I'm having the same issue.

If I start the game with Battleye enabled, any keypress brings the game down to 0 fps (happens even in the main menu), and after releasing the key it takes a bit to catch up and get back to the usual fps.

This happens only with the keyboard. I haven't noticed anything wrong with the mouse or even a controller, and I tried more than one keyboard.

It might be the same thing as issue #0024435, but I tried updating drivers and running a malware scan, but it wasn't fixed