I don’t think the Russian warships will engage US warships at first anyway. If they are not shooting they won’t be shot at. That job is for the P-800 Oniks the Russians sold Syria, fired from Syrian shore, then Russians are only observers as the US ships fight for their lives, and Russia stays unencombered for at least the first engagements.
And Russian arms on the way could be more of these sort of antiship missiles, and advanced SAMs and even the Russian technicians to target and fire them, so as to be used on short notice without having to take time to train the Syrians in their use. As far as the US is concerned there is no way to know the nationality of those using the shore based weapons, unlike a weapon originating from a Russian warship.
I think the Russian warships are there for symbolic reasons at this point, but also to mop up and engage later in the crisis as it develops. And as it escalates, introduces a tactical nuclear capability at sea that the US lacks as a trump card. (The US removed all tactical nukes from non strategic naval platforms in 1991, Russia was suppose to as well, but has been reported as retaining that capability and weapons in reserve, and could plausibly be deployed with the Russian ships)
The Israelis knowcked out most, if not all of those missiles a couple of months ago in an attack on the port aimed specifically at those missiles.
Also, those missiles, while very dangerous, have significantly less range than our Tomahawks, so our ships can stay far enough out to sea to be able to hit all the targets in Syria without coming into range of those missiles even if Syria has some left.
Those missiles would be a lot more dangerous to us if they were able to be loaded on the SU-24s or Mig-29s Assad has...but that capability never arrived in Syria and the aircraft have not been upgraded to launch them. The Yahkonts have a range that is comparable to our Standard Missile defenses on the AEGHIS destroyers, so aircraft carrying them may be able to launch them without haveing to enter the kill envelope of the SMs.
But, they did not get that capability, and as I said, the Israelis got most, if not all of those missiles anyway. Any they have left would be launched from shore and we will simply stay out of their range.
Now, the Syrians have 75-100 Kh-31 missiles, which they can load onto the SU-24s and Mg-29s. They too are danerous weapons. But their range is signifcantly shorter than the Standard Missiles the AEGIS destroyers are firing and so the aircraft have to fly quite a distance into the Standard Missile envelope and are going to get hammered before they ever launch. We have all the advantage in such an engagement because our AWACS will see any large group of aircraft taking off, forming up, and coming out against the US vessels. We will be ready for them.
If we do not have our own aircraft up out of Italy to intercept them, or the French carrier aircraft do not intercept them (which I believe they would) then they still have to fly fairly deep into the combined weight of five AEGIS destroyers missile defense before they can launch.
I do not believe Assad will throw away his entire modern air force to take the chance (and a bad one at that) that he might get a hit from any of those Kh-31s.