I was doing tool use before chatgpt released an official API for function calls. You literally give ChatGPT API specs and ask it to generate call parameters.
The API is fed into the LLM as context, the response is part of the output. Whether you pass that output through another layer of LLM is trivial. And even if you do, the "context" in that case would be only the response, not the whole database. You are confusing even yourself, you accepting the overloading of the word 'context' (pushed by a company for commercial purposes) and you are now unable to distinguish between LLM context in terms of tokens, an external data source, and a response fetched by the tool.
It's not that I am ignorant of what Anhtropic claims Context means, I'm contesting it. If Microsoft releases a new product and claims that Intelligence is the parameters of their Microsoft Product, then it pays to be a bit cynical instead of parroting whatever they say like some unpaid adman