But you don't explain, in any of your comments, precisely how an LLM in practice is able to itself invoke an API function. Could you explain how?
A model is typically distributed as a set of parameters, interpreted by an inference framework (such as llama.cpp), and not as a standalone application that understands how to invoke external functions.
So I am very keen to understand how these "major models" would invoke a function in the absence of a chassis container application (like Claude Code, that tells the model, via a prompt prefix, what tokens the model should emit to trigger a function, and which on detection of those tokens invokes the function on the model's behalf - which is not at all the same thing as the model invoking the function itself).
Just a high level explanation of how you are saying it works would be most illuminating.