I've also been trying to find documents and movies about the Apollo missions that are more about the engineering than the people. (Nothing wrong with the latter, just feels like that's all the existing, sometimes over-dramatized films are about).
Like this technical memo about Apollo data network systems from 1966: https://ntrs.nasa.gov/citations/19670009662
JPL specifically has its own repository with similar content at https://dataverse.jpl.nasa.gov/dataverse/jor
Like this paper about file transfers with the Europa Clipper spacecraft: https://dataverse.jpl.nasa.gov/file.xhtml?fileId=72593&versi...
You could do worse than just reading all the Wikipedia articles on all the various pieces of hardware, e.g., the Lunar Landing Research Vehicle
https://en.wikipedia.org/wiki/Lunar_Landing_Research_Vehicle
For a film that's meant for entertaining, this is all you well ever see. The drama is what the mass audience can understand. The mass audience will not grasp the majority of the science/engineering and will get bored.
There are some very science oriented content, but their popularity is dwarfed by the dramatic stories of the people. It's just like what true hacking in films is mostly just made up stuff to look cool rather than just the boring work that hacking truly is because nobody will watch it. They might as well cut to a YouTube stream of someone live coding.
There were plenty of critical moments and plenty of drama. Ironically, for all of the manufactured scenes about discrimination and rejiggering of timelines by decades in the movie, John Glenn apparently did ask for Johnson to check some calculations ... he just didn't do it during final launch prep.
The wikipedia page on the topic has a great list of "things that didn't happen that way" in the movie:
https://en.wikipedia.org/wiki/Hidden_Figures#Historical_accu...