It's dangerous to extrapolate much from the performance of the Russian Navy in the Black Sea. While Ukraine has had remarkable success in almost completely shutting down Russian naval activity in the Black Sea, it's not all due to the superiority of drones. Russian incompetence, both in naval strategy as well as operations is endemic, and the fate of the Moskva and other systems isn't indicative of a widespread vulnerability of surface vessels to drone systems. The Moskva was sunk with cruise missiles, primarily ones developed from Soviet era missiles (Kh-35). Much has been written about the materiel state of the Moskva, as well as operational decisions/inadequacies that lead to its demise.

Surface drones work well when air cover is limited/restricted. Tracking them via radar is difficult due to surface noise, but it can be done. Countering them isn't an impossible task either, it, like other threats are handled systematically. The Russians have a relatively slow OODA loop, and Ukraine has been very successful in leveraging their superiority.

Is the threat a universal one or limited to the UKR/Russian conflict? A little of both. We've seen where an unprepared ship can be easily damaged by a small boat laden with explosives (USS Cole). We've seen the Ukrainians shut down Russian activity in the Black Sea, even going so far as to down unwitting aircraft that didn't respect the threat. But militaries adapt, especially to proven threats. Witness how the West responded to the sinking of the Eilat in 1973. It developed countermeasures and weapon systems for the threat of cruise missiles, while simultaneously developing their own cruise missiles (Harpoon/Exocet/Otomat/Penguin).

Will undersea drones prove as concerning? I doubt small swarms of UUVs will proliferate like we've seen with FPV drones. Flying through the air is much much easier than operating in water. Propulsion, C2, and targeting is quite difficult underwater compared to UAVs. Both range and payload are a challenge, so I don't believe that a swarm of "small underwater drones" will be able to detect the quietest ships in the ocean any time soon, much less track and trail something that can travel at speeds above 40kts with ease.

Now will large UUVs have a role in future naval combat? Undoubtedly.