a disclosure before I get started: I'm not very familiar with the minutiae of wetland or coastline tagging. This changeset broke rendering of the bays, so that's why I reverted it.

natural=water represents the area of water features inside the natural=coastline way. The natural=coastline way should go roughly at the "mean high water springs mark". Since the natural=coastline way is at the outer edge of the barrier islands, a natural=water tag is needed for these areas. You can see the current coastline tag here: https://www.openstreetmap.org/way/440522406

Whether the mainland should also have its own coastline is something I'm not sure of. I recommend hopping in the OSM US slack ( https://slack.openstreetmap.us/ ) or the community forums ( https://community.openstreetmap.org/ ) if this is something you're interested in.