Did you play a specific system?

Honestly I don't use them for much RP these days, mostly novel-style writing instead :P.

most online options

'Online' systems are probably taking bone stock LLMs and using 5e rules banged into the system prompt anyway. You could do the same thing with with a local UI (like Kobold, Open Web UI, mikupad. Take your pick.)

I’m curious if you can teach these other systems and settings, that would be awesome.

Theoretically? You could collect some text from completed Cyberpunk RED games and finetune a model.

Or maybe use constrained sampling to help it format certain answers, which would be much easier.

But honestly I would just try some 'strong' models and see if they follow the rules you paste into the system prompt, unless you want to dump a ton of time (and some cash) down the finetuning rabbit hole.