Sort of. It was part of GNU, now it's sponsored by the GNOME Foundation, but I don't think it is considered a "GNOME App".

As per https://discourse.gnome.org/t/relation-between-gimp-and-gnom...: "The GNOME Foundation provides the GNU Image Manipulation Program community and developers with services like fiscal sponsorship, technical infrastructure, promotion, and copyright assignment."

However, it's not considered a GNOME "Core App" or even a "Circle App" (see https://apps.gnome.org/) and I believe that it doesn't attempt to follow the GNOME guidelines or have any GNOME designers/developers working on it.

GNOME originally stood for GNU Network Object Model Environment, so both G's are in some pedantic sense the same.

I don't think there's a very close relationship between GNOME and GIMP, but do keep in mind that GTK, the 'defining' part of GNOME, originated in GIMP (Gimp ToolKit!)

Gnome's toolkit, gtk, originated as the toolkit the gimp folks wrote to get off of Motif a long time ago. Since then the Gs have had reassigned meanings.

Yes https://gitlab.gnome.org/GNOME/gimp