I think there is a misunderstanding from your side the first link you mentioned is of the gnome extension which is designed and built for core22 while the second link states of gnone-3-38 which is built on core20, in short both extension are different [gnome vs gnome 3-38]
Euh I kinda get what you are saying, but it looks awfully confusing. The page is titled “The gnome extension” and literally reads
This is an updated version of the gnome-3-38 extension that will only work with the core22, built from Ubuntu 22.04 LTS.
So as a random reader I’d reckon the page is just about the Gnome extension. There’s no indication it’s somehow about core22 (or any other core for that matter), and it’s also not clear the page is about a successor to gnome-3-38 (which is what you’re hinting at I assume).
Anyway, I’m totally lost in this “core vs gnome” versions conundrum, and I’m just unable to build Ymuse as I fail to find a working combination of core-gnome-gotk3 flags…
The gnome Core22 extension contains GTK3 libraries, it’s functionality equivilent to Gnome-3-38 in Core20.
It also contains GTK4 / Gnome 42 libraries, making it also viable for GTK4.
Gnome-3-38 in core20 doesn’t support GTK4.
This is what’s meant by Gnome is an “updated version”, but gnome won’t work for Core20. You’d either want gnome-3-38 for GTK3 or if your app does make use of GTK4, you’d set the base to Core22. Whether GTK3 or 4, gnome on Core22 would cover both.