I did not manage to produce any logs. However, what I did manage was to upgrade Mesa on Ubuntu 20.04 from the 21.x branch to the 22.x that both Fedora 36 and Ubuntu 22.04 are on.
Ubuntu 20.04 with Mesa 21.x –> works fine without any problems
Ubuntu 20.04 with Mesa 22.x –> same type of graphical issues as with Fedora 36, Tumbleweed and Ubuntu 22.04.
(I also tested Linux Mint 21 XFCE which had the same problem so this is not related to GNOME).
It seems very likely that the issue with NoMachine is related to the Mesa drivers.