It seems weird to me that you'd want a model per API to be trained rather than a model that understands many APIs. There's likely more similarities than differences in that the differences are really your domain model which infects the nouns of the but less so the verbs and structure.
I played with building out a graphql mesh [0] of a few different APIs as I was curious to see if I could build one schema (and subsets of it) and have GPT interface over that. Turns out, it did a pretty good job if you can provide it the right portions of the schema it needs.
It also helped out when I was struggling to reconcile with how large of JSON payloads I was getting. The REST endpoints are just killing the prompt size, but having the model choose the fields it needed from GraphQL really helped out there.
Put it down for a while until I can get access to the plugin fine-tuned version of chatgpt and see if there's still a need or if it is additive still.