If you want to read a few interesting takes by Sci-Fi authors themselves on the subject...

https://www.tor.com/2016/01/21/how-do-you-like-your-science-fiction-ten-authors-weigh-in-on-hard-vs-soft-sf/

First off one could make the divide between "Science Fiction" or "SF", and "Sci-Fi".
SF usually means "Hard" SF grounded in science, while "Sci-Fi" *(coined by Forrest J. Ackerman who had rather vulgar taste) is more like western stories in a SF setting, or simpler adventure/action stories, or space operas.

One could also make the divide between the "Hard" and "Soft" sciences, so stories dealing with psychology would be "Soft SF".
So writers like Asimov, Clarke and Clement would be Hard SF, while Philp K. Dick is soft SF, and Ray Bradbury is Sci-Fi.

The rather silly "Science Fantasy" term could be applied to things like Dune and Star Wars, which mixes Fantasy and space opera.

Do the later Final Fantasy games from about 6 onward count more towards Science Fantasy than just fantasy in general?

I do not think the problem is not to understand what you want to communicate. Its that you refuse the very real existence of a major franchise like Shadowrun which does have a LOT of very hard SciFi elements because of its cyberpunk half mixed with D&Desque high fantasy. The very tangible artificial cyberarm prothesis does not become any less hard scifi because an Orc has it and a Dragon owns the company that builds it. Just saying that makes all that automatically fantasy too while your right to believe and to say does not make that true.

Thats what I meant previously by Shadowrun being a clash of two polar opposite extremes.

It really depends.

6 has fairly mild technology elements compared to many of the later ones. Aside from Narshe and the Empire, the world is pretty much fantasy. (Figaro Castle's ability to submerge is something I would accept in fantasy with limited technology.) In particular, I note that high technology does not dominate the game world. Furthermore, the technology level is more steampunk, sort of like Arcanum, actually.

FF7 (which I played but didn't like) and FF8 (which I haven't played) take the technology level further, to the point where it no longer feels like fantasy. We also see this sort of thing later in the series (with FF15 using a *car*, of all things, as a mode of transportation).

FF10, from what I have seen in videos, feels more like the "fantasy with ancient technology", though it doesn't feel like classic FF.

FF9, FF11, and FF12, on the other hand, are more the traditional FF "magic with ancient technology" setting. (I note that FF9 still has more technology, though not in a realistic manner, than FF1-5 seem to.) These games, setting wise, are more like classic FF. (Though I note that FF11 is not even in the same game genre as most of the series; it should have been called something like Final Fantasy Online, with FF14 being Final Fantasy Online 2.)


Edit: I should mention one thing: The only post-FF5 FF games I have played are 6, 7, and 9. I have seem lots of videos of 10 (especially challenge videos, like No Sphere Grid boss fights) and a few of 8 and 12, bu t I haven't actually played them. FF6 is the last FF game I have actually beaten, and even then I don't like it as much as the early games in the series (and I place the cut-off between FF5 and FF6).