Most experts say that someone who has recovered from Covid is no longer infectious 10 days after onset of symptoms. That said, recovered Covid patients may have a positive Covid result on a PCR test even several weeks after recovering from the illness. (I'm not sure if this is true for the antigen test.)

Does the government of St. Maarten allow entry of vaccinated U.S. visitors who recovered from Covid a month ago -- without requiring a negative Covid test? Because a negative Covid test may not be available for such a person.

SXM does not differentiate between types of passengers arriving from the US other than by age (children) . Everyone needs some kind of negative test to enter. I believe documentation of COVID recovery is ok for a return to the US