hdmi works fine for HP Envy (two different laptops, one with 22.04 and one with 20.04 ), and another one with exactly same (Clonezilla) partition of ASUS TUF 22.04.
On a smaller monitor HDMI I can get, switching to xorg (X11) full screen but severely bad quality. I did have half a screen earlier on. System bogged down a lot too, mouse and keyboard. On a larger 60" TV, nothing Wayland or X11.
Nothing for either on Wayland.
nothing in BIOS for HDMI. Secure boot is disabled. Legacy enabled.
https://www.asus.com/us/supportonly/FX505DT/HelpDesk_BIOS/ BIOS 3.16 latest I have it.
other threads here go back to 2016 on this sort of problem.
gnome is 42.4 kernel is 5.15.0-48-generic updates up to date.
side note: sad that this is a gaming laptop.. and a huge improvement over the other struggles with the Envy's over three years (you name it, I've had it).