You ban them from coming back in after a few warnings. Stores seem really icy about facial recognition right now though. The optics are pretty bad (a play on words pun?)

Who is going to stop them from coming back in?

There have been a few stores that won't really stop people from coming back, they just quietly file charges, and then the person finds out next time they get pulled over or something along those lines.

No one, they get automatically flagged, and then someone asks them to leave. Or the police are called and they are trespassed.

You install AI-powered turnstiles at the entrance. Come on haven't you seen or read any dystopian media? :)

Use your army of lawyers to help file misdemeanor theft charges of course. Then get one out of 100 of the defendants who actually has something to lose to pay big damages to fund it to happen again the next time.