If you're a regular there, I think it's reasonable to contact them and say that you go there often and are bothered by the AI. "I started coming here regularly because it felt authentic". "You guys don't feel authentic anymore, and I'm disappointed" or more strongly "and I'm thinking of taking my business someplace that cares enough about their customers to put in the effort." "I wish you'd go back to the way you used to do things." Etc.

Assuming we're really talking about a small business, it's very possible someone will listen.

I reach out to small businesses all the time working on OpenStreetMap, and (obviously with selection bias for the ones who respond) they're usually just pretty nice-seeming people trying their best with what they have.

Edit: One thing I think I should've emphasized isn't just to say "please stop using AI" but that specifically "I liked it better the way you used to do it." or outright, with no comparison, "I liked the way you used to do it". "It made you unique." That is, give them a concrete alternative. For a lot of people, AI, like plagiarism (because it is), is a tool used when someone thinks their voice isn't good enough. It helps to try to convince them that it is enough and that they not only don't need AI but that it's harming the unique identity you enjoyed by making them blend in with everyone else.

Edit 2: I didn't think to include this before, but like obviously, be honest. If it won't upend your business there, don't say that it will; consider real effects it'll have, like "I don't know that I want to recommend this to friends anymore." If you've only been there five times, don't be afraid to say that; "I've shopped/eaten/whatever at your establishment several times, and [...]". If you're asking somebody to be authentic, you not only owe it to them to do the same, but it's probably a more effective strategy. They'll probably be more moved by Bobby Jones (43) who likes to come in for a burger every couple months after work and just doesn't like the vibe anymore than their biggest fan they've never seen, the oilman in from Dallas who spends $20,000/month at their establishment and is so simply appalled that they cannot in good conscience return until the Burger Shack de-lobotomizes their mascot design.