Do you know what happens to explosives on sunk ships generally? Are they usually left at the bottom of the ocean, and could they have the potential to detonate?
So yes there is potential to detonate, but in general that does not matter a lot unless you are the unluckiest person in the world and happen to be right above it at the time. The explosive wave front expands in a sphere and so decreases in amplitude with the square of the distance to the origin. It loses lethal potential very quickly.
SS Richard Montgomery comes to mind. Tsunami threat directly off the southern coast of England.
As far as I know, nobody has tried to retrieve conventional munitions from a shipwreck, and reasonably enough - they're not dangerous enough to be worth the trouble. Nations will go after lost nuclear warheads, though; indeed, Bayesian search theory saw significant development and interest to serve that purpose [1], and the CIA's been known to go to Bond-movie levels of trouble to the same end [2].
Granted, these were both First Cold War projects, but it seems like there's some degree of possibility that this use of "First Cold War" may eventually prove not to have been a somewhat silly joke, so...
[1] https://www.lesswrong.com/posts/RTt59BtFLqQbsSiqd/a-history-...
(For what it's worth, I don't love linking to Less Wrong for this or any reason, but I couldn't as quickly find another reference for the point about Bayesian search theory. If not for the fact that I've seen it mentioned elsewhere in, let's say, less breathlessly wide-eyed technopositivistic contexts, I wouldn't have included it at all.)
I admit that I'm triggered by Less Wrong, though.
With regard to the value of recovering Moskva, I suppose I don't know. It's not all that young a design, and evidently struggles against even subsonic antiship missiles. Not that that means it's worth nothing, of course, but I could see the possibility that to attempt a recovery would be throwing good money after bad. That said, you quite evidently have experience in this realm that I lack, and your analysis is thus certainly better informed than mine.
And since it sunk in the Black Sea, depending on the exact location, it could have sunk in a relatively shallow area, where it is easy to do the salvage even if there is no really good reason.
The Israeli Navy, for example, spent several decades searching for its lost submarine INS Dakar. It was located in 1999 and then the conning tower was salvaged from a depth of 3,000m and placed in the Naval Museum.
That makes it worthwhile to try and prevent the enemy from seeing that tech.