Yes, Russia is making advances in the eastern Mediterranean Sea.
But even if Russia has more capacity to force the Turkish straits than the Soviets had (or if Russia can turn Turkey away from NATO), NATO now has the geographic position to contest Russia's forces in the Black Sea:
A NATO flotilla arrived in the Black Sea on Wednesday to train with ships from the Bulgarian, Romanian and Turkish navies, the U.S.-led Western alliance said.
It is just 6 ships, including one of our missile cruisers, but it reflects that we have a position on the western shore of the Black Sea now, with Romania and Bulgaria as NATO members.
Add to this the Turkish control of the southern shore, Ukraine's control of the northwest, and Russia's lack of control of all of the east where we have the potential of having a presence in Georgia (not a NATO member but a friend).
Of course, I think air power from all these land areas is the best threat we can pose to Russia's control of the Black Sea. Even as Russia makes a play for influence in the eastern Mediterranean Sea, their power to exercise influence is a peacetime-only power.
If it comes to a shooting war, Russia's Black Sea military power will be fighting for its life and not worrying about supporting anything in the Mediterranean Sea.