I don’t see what business NATO would have in the Caspian if none of the nations around it are members of NATO.
Also, if we’re to argue that NATO has a right to be on the Caspian anyway then Russia has a right to be on the Great Lakes.
From that map, it would be a lot easier for them to take the St. Lawrence Seaway right to Detroit than for us to sail up into the Caspian Sea. They make an excellent vodka up there, BTW.