Can you actually swim at their beach after you enjoyed a dinner?

Yes you can. A lot of people swimming the day we were there.

Yes

I did too

While dining I did see three or four people wading in the water and no one said anything to them

You may walk the beach and dip your toes in the water, but the beach is now dedicated to dining only.

You aren't allowed to swim technically, but you can stay and walk in the water. The kids were swimming and no one called them out.