I suspect that people instinctively believe they have free will, both because it feels like we do, and because society requires us to behave that way even when we don't.

The truth is that the evidence says we don't. See the Libet experiment and its many replications.

Your decisions can be predicted from brain scans up to 10 seconds before you make them, which means they are as deterministic as an LLM's. Sorry, I guess.