Try and see if the settings application shows the onscreen keyboard as enabled or not. Should be in All settings- Virtual keyboard. If it was working on the lock screen it might just need some setting to change. Are you on X11 or Wayland? That might also be a factor, if it stops once it switches display servers.
Hey, glad to see you got it semi-working now. For the keyboard config inside SDDM, I know of arch instructions, but it should work the same on yours. The package to install for the virtual keyboard might be different, but the config file for SDDM should be around here ( says to make it if it doesn’t exist)
https://wiki.archlinux.org/title/SDDM#Enable_virtual_keyboard
The specific package on Debian seems to be this one. Try installing it with all dependencies needed-
https://packages.debian.org/sid/qtvirtualkeyboard-plugin