Here’s what I was told in an email today from the Office de Tourisme de Saint Martin. I’m not sure what to expect.

Please find traveling restrictions and advice for entering the french territory by plane:
http://www.saint-barth-saint-martin...s-d-entree-par-voie-aerienne-et-maritime
unfortunately the internet site is in french.

You are not required to take a rapid test once on the island neither to travel one side to either.

Once on the island there is no border control between french and dutch side, you are free to circulate one side to the next.