California-class ships are weirdly huge. The way people talk about their missions and status , I initially thought they're meant to be smallish starships, like Intrepid-class, but they're almost Nebula-class size. Plenty of room inside those pylons for multiple lift shafts.
There are hundreds of such LLMs with published training sets and weights available on places like HuggingFace. Lots of people run their own LLMs locally, it's not hard if you have enough vram and a bit of patience to wait longer for each reply.
showrunners said they would like to, but it's not happening.
there was a brief TAS style animated ad for the resort planet in episode s04e03.