From my privacy trials on ollama - any model downloaded does not know the date or time and cannot access the internet.
If you are still sceptical you could download something like alpaca on flathub and once youve acquired a model, remove internet access etc through flatseal.
theres a cool preset called "futuristic" on the linux version (cool retro term) -with a bit of tweaking you can make it look like a terminal from the alien franchise
Its a great intro to a more privacy focused ROM than stock android - I got one for a friend who's never used any other custom ROM before and he loves it.
Ive been meaning to flash this onto my fairphone but the websites instructions are a bit confusing (I've installed calyx, eos and graphene on other phones)
that makes sense, thanks for clearing that up