How to build custom (verified) integration?

I offer a service where users can finetune custom LLMs through conversation (just telling how they want it to act, and really updating the weights behind the scenes!). I want to seamlessly integrate this into lovable; I am willing to do all the legwork, but want to understand what steps I would need to follow to accomplish this and make it super easy for users of Lovable.

The API works basically the same as the standard OpenAI-style inference API, with special endpoints for model creation and teaching.