As you yourself say, the context is the text that is fed as input at runtime to an LLM. This text could just always come from the user as a prompt, but that's a pretty lousy interface to try to cram everything that you might want the model to know about, and it puts the onus entirely on the user to figure out what might be relevant context. The premise of the Model Context Protocol (MCP) is overall sound: how do we give the "Model" access to load arbitrary details into "Context" from many different sources?
This is a real problem worth solving and it has everything to do with the technical meaning of the word "context" in this context. I'm not sure why you dismiss it so abruptly.