When using the Snap of Gzdoom, it can be challenging to find where to put the wads. But this is due to the Snap architecture. But this is in the snap folder in your home directory.
This is the location.
snap/gzdoom/121/.config/gzdoom
Put the doom2.wad file in here and it will be accessible in the menu.
┏jcartwright@jcartwright-System-Version╼╸╸╸╸╸╸╾ ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━◉:~$ ls -hula snap/gzdoom/121/.config/gzdoom total 54M drwx------ 2 jcartwright jcartwright 4.0K Jan 21 20:46 . drwx------ 9 jcartwright jcartwright 4.0K Jan 22 2024 .. -rwxr-xr-x 1 jcartwright jcartwright 14M Jan 21 20:46 doom2.wad -rwxr-xr-x 1 jcartwright jcartwright 12M Jan 21 20:46 doom.wad -rwxr-xr-x 1 jcartwright jcartwright 28M Jan 21 20:46 freedoom2.wad -rw-rw-r-- 1 jcartwright jcartwright 17K Jan 21 20:46 gzdoom.ini
This is a very simple solution when using the Gzdoom snap on Ubuntu.