You have to drive over to the ocean for an actual beach but it’s only about a mile away. We put our kayaks in right from our campsite and was very shallow on our side so I think you would be able to swim there. However you would need to check their rules regarding swimming from the campground to see if it is allowed
You can swim at the beach at the park up the road from the campground. The water off the campground is shallow and grassy but great to sit your chair in and relax. People do get wet in the water yet the beach up the street is beautiful.
In the campground lagoons? No...oyster beds and wildlife make that difficult but the paddling is great. But the park beyond the campground has miles of beautiful sand beaches on Tampa Bay and the Gulf of Mexico.