Eli5: isn't this a regular thing? Like ships are gonna ship... That's what they do. I don't think an American ship is going to attack any Russian if they are not being attacked themselves?!? But please eli5
this is NCD, so anything is possible, but in a more serious way of thinking, Turkey is still a member of NATO so even if US fleet can't enter the black sea, they can stay in national turkish water as long as Erdogan does not explicitly eject them and having a US fleet inside the Bosphore is a good way for US to show muscle and put pressure on any nation bordering the black sea without even entering the black sea.
The USS Mount Whitney is an amphibious command ship, so there's no way she's going anywhere near the Russians. However, she is also the Afloat Command Platform for NATO Naval Forces, which might signal further NATO intervention to protect shipping lanes...
She's also chock full of high end sensor and communications gear, and probably being used to gather and disseminate intel on Russian air and surface movements.
Come to think of it the USA and the British Empire before them draw their power from controlling the oceans and ensuring international trade goes smoothly and brings them coins. If a certain someone starts shooting left and right at legitimate merchant ships it's kinda a matter of credibility to show up for "the maritime power".
Is the US Navy even a maritime power though? Aren't they more of an airborne power these days, given they have the second largest fixed-wing air force in the world (right after the USAF)