Hi, and sorry for the long delay.
I reproduced this in a clean Debian 13 VM: it is two separate problems,
neither caused by
turning the on-screen keyboard on.
The black desktop and the dead right-click are there already at login,
because Debian
installs no XWayland with Cinnamon: nemo-desktop, which draws the
wallpaper, the desktop
icons and the desktop context menu, is an X11 client and dies with
"Cannot open display".
Installing the xwayland package gives a normal desktop, keyboard still
enabled. I filed
that separately as #1147594 against cinnamon-common; it affects that
session whether or
not you touch the keyboard.
The keyboard is responsible for the third symptom: on 6.4.10 it opens as
soon as you
enable it and stays on screen covering the top third of the display,
even with "Show
keyboard only when the user activates it" — so anything up there becomes
unreachable. It
does the same on X11, so it is not a Wayland issue.
That part is fixed. The on-screen keyboard was rewritten upstream in
Cinnamon 6.6.0, and
with 6.6.9 in unstable enabling it leaves the screen alone. The first
6.6 upload to
Debian was 6.6.7-1, so I am closing with that version; the rewrite is
far too large to
backport, so on trixie the keyboard will keep behaving as you saw.
Thanks for the report.
Fabio