Are you sure? Im pretty sure Ive seen pictures of the Admiral Kuznetsov (~70,000t) in the black sea. Besides, ships much larger than that (Oil tankers) also pass through there dont they?
Re the tankers the tonnage limit applies only to warships, not merchants. I’ll have to see what I can find about the carrier provision. I remember this being a big thing in the ‘70s with the Soviets insisting their early aviation ships were in fact “cruisers” in order to be able to pass through to the Med.