in my opinion, yes, this is exactly what this relationship is intended for
there is an opposite case too, as unless they were also included, tracks from a “music inspired by” soundtrack would likely not get this relationship (or any other soundtrack release tracks that didn’t actually appear in the film or show, unless maybe they were written for it and were cut)
I’d have to give it a closer listen, but the only commonality I hear between all of these (save for Legends Arceus and Scarlet/Violet, obviously) is the melody. the harmonies and rhythm/bass parts are quite different in most of these. a possible exception I heard on a second listen is that Diamond/Pearl and Brilliant Diamond/Shining Pearl do have a similar arrangement (there could be more, I’d have to give it another few listens)
I did a deep dive similar to this about a year ago for Gourmet Race / Dreamland / Fountain of Dreams (depending on the game), which has basically become a main theme of the Kirby series
as to the rest, we might be getting a bit off-topic to this thread, tho I’d be down to discuss it in a new thread. tho I will say I feel that VGM (and soundtracks in general) might be its own thing between popular and classical, too classical to be popular, but also too popular to be classical (or maybe a subcategory of both)
on a similar note, one outstanding question I have is if a cover or arrangement of a piece is made for a soundtrack (or musical or whatnot), should that get a new work and “part of” relationship, or no new work and an “included in” relationship?
one such example is Holding Out For a Hero from Shrek 2. it’s a cover of the Bonnie Tyler song, but in a different style, and it interpolates the heroic theme from the previous movie (you can hear it when Shrek comes riding in on Mongo, the giant gingerbread man)
I think I personally favor creating a new work in cases like the above, where there’s other works interpolated, but for cases where there’s not as significant a change in the music, I’m not sure where I stand