These are just symptoms. HDMI doesn’t work properly for you, wayland doesn’t work properly and x11 doesn’t work at all - the whole graphics system doesn’t work properly.
Now we are one step further.
Upload again a complete journal and a current Xorg.0.log (and if available Xorg.2.log).
Boot a garuda-live.iso with selected proprietary nvidia drivers and check if there are any issues with x11/wayland/HDMI.