here's a good article explaining the situation. it not a size thing for a carrier group per se in the Black Sea, but a "max tonnage of a warship permitted" issue.
https://gcaptain.com/us-navy-aircraft-carriers-ukraine/
once you're through the Strait, the Black Sea isn't a small body of water from the looks of it.
we've had cruisers and destroyers there before but carriers are banned by treaty. sounds like it's basically up to Turkey's discretion. obviously, carriers aren't needed to protect a grain ship lol. cruisers, destroyers or frigates would do nicely if we could get Turkey on board, which is a big if. they're one of our flakier NATO allies, to say the least.