Have you tried defining your keyboard layout in "/etc/lightdm/lightdm.conf"?
Adding the following in the "[Seat:*]" section will do the trick:

display-setup-script=setxkbmap de

Alternatively, you can add the keyboard selector to your lightdm panel. That'll allow you to change the language on the fly

idk, haven't tried it - someone would like to?

but still, it's easier to have a script. One Code for everything.... so you don't have to switch everything (just the default lang) :-)

Greetz

Since Kali 2022.1 the keyboard layout selector is placed in the top-bar of the login screen.

To change the system keyboard setting you need to run (and then reboot):
sudo dpkg-reconfigure keyboard-configuration

Captura de pantalla de 2022-02-17 15-31-22.png (133,141 bytes)   

Captura de pantalla de 2022-02-17 15-31-22.png (133,141 bytes)