By the shape of this cay I think it is Matt Lowe's Cay.
Interesting that they say "seven private beaches," there are no private beaches in the Bahamas, all are public below the high water mark.
Could be they are going to try and make it uncomfortable for anyone going ashore - like Baker's Bay tried to do.
We anchored off there for a night in 2018. There was development ongoing then. We set up on the beach and we're driven off by three guard dogs. I meant to complain to the authorities in Marsh about it but never did. Story in the blog entry below.
Beautiful Beaches, Fabulous Bars, And Mad Dogs And Irishmen | AtAnchor.com