I’m not a fan of these films but I’ll clear up a couple of things:
https://www.youtube.com/watch?v=yn21u6j6Ywc
It’s shot on 35mm, so it’s absolutely 4K+ if you’re scanning the oneg. 2K film-out is 2048x1556 and that was the standard since Terminator 2 and Jurassic Park. Before that I believe all CGI had not been attempted to be printed full-frame, that is to say that Abyss and anything older had CGI printed that was then optically matted into the negative.
The first film from the video above does not have a DI, that means it’s photochemical and therefore yes it’s higher than 1080p. The final release prints are probably in the range of 1.5-2K and remember that 2K means 2048x1556 NOT consumer 2K at 1920x1080/2048x1152. The second and third film had DIs, that means 2048x1556. It doesn’t matter what resolution the CGI was rendered in - the CGI can be rendered at 1.5K, 1080p, 720p, whatever. The CGI is simply being added to the 35mm background which would have been scanned at 2K (2048x1556) and the DI will be 2K. Some further information is here:
https://thedigitalbits.com/item/lord-of-the-rings-trilogy-2020-4k-uhd
The Fellowship of the Ring was shot photochemically on 35mm film in Super 35 format using a variety of Arriflex, Arricam, Mitchell, and Moviecam cameras with Zeiss Ultra Prime and Angenieux Optimo lenses. Only about 70% of the film was finished as a Digital Intermediate at the time, as the process was then new and still evolving (the other 30% was finished traditionally on film). For this new Ultra HD remaster, Park Road Post (a New Zealand post facility owned by WingNut Films) went back and scanned the original camera negative in 4K, then scanned the VFX film-out elements (for VFX shots that were finished on film) in 4K, and upsampled the VFX shots that were finished digitally (in 2K resolution) to create a brand new 4K Digital Intermediate at the proper 2.39:1 aspect ratio.
That’s describing the type of CGI in Abyss and older films: VFX that is rendered and then optically matted into the film. Also it doesn’t matter how much was DI and how much wasn’t, the VFX doesn’t set the resolution the background frame does.
The resolution of the final prints will vary. Terminator 2 projected off an original 35mm which I have seen on a huge 70ft+ screen (I’d have to do some digging to find the exact size, but it’s at the size where the difference between 35mm and 70mm is very obvious even with the sharpest of 35mm) and it is clearly 1.5K or lower true resolution perhaps as low as 1K. Most 70mm makes 4K look like low resolution. So as with anything with prints, it’s a matter of YMMMV depending on where it was printed, whether the cinema had a large screen and demanded they print it to a higher standard than a multiplex cinema which was the standard at the time (and sadly still is). So for example it’s possible to print your standard quality for multiplexes and then do some at show-print quality for the Theatres that still had large screens.
Re: your last point I remember seeing Jurassic Park at an IMAX back in the 90s and it looked terrible because they were taking a regular print that was definitely not meant to be blown up that big and doing so.