Keyboard Backlit control not showing on Gnome 45.2 Desktop Quick Settings

The issue you are having is Framework specific. I clicked your link, which leads to a Fedora Post on this forum, but your issue is not Fedora specific as that Post links directly to a Framework forum post rabbit hole.

It is apparently a known issue with that specific keyboard make/model laptop.

Which also leads to :

Which could be a side effect to why Gnome Settings is not displaying a control for a Fn operation that is probably not in use or recognized by the system.

I would recommend finding a solution to your Fn key issue first. Frame work forums has apparently solved it somehow.