It is autonomous in the sense it can continue to function without supervision after the operator has started it, in the same way countless programs on your computer are “autonomous”.
But it can never choose to begin doing something at any time of its own volition. It does not have “autonomy” like a human does.
Humans are not autonomous: they're not even your employees until you hire them. (This is what I understand you're saying about AI.)
"It doesn’t even exist until you ask it to do something", not my words
If you don’t believe in free will then nothing is autonomous.
Something like NASA's Mars rovers are considered as semi-autonomous since they do receive external instructions, but then execute those instructions autonomously without further intervention. Similarly the combination of a coding agent and the LLM it connects to would best be considered as a semi-autonomous system.
You could also have a fully autonomous robot, or just agent, powered by an LLM, where it's not taking external instructions, but rather reacting to external events in some internally proscribed way.