I also noticed that the problem only appears when using X11 (i.e. with SDDM or when running an X11 session of KDE Plasma), on Wayland and in TTY everything works.
UPD 1: I’ll try to get rid of X11 in SDDM.
UPD 2: I was able to work around this problem. I wrote the following in /etc/sddm.conf.d/nvidia-fix.conf:
[General]
DisplayServer=wayland
[Wayland]
CompositorCommand=weston --shell=kiosk
Having previously installed the weston package. There are still issues with the two keyboard layouts, but I might get to that later (I’ll update the post).
However, the issue is not completely resolved, so I will not mark it as such, hoping that this will influence the appearance of a fix.