The only specific one mentioned in the story was the Soviet SSN sunk near the Andera Doria. However much of sinkings occurred in the deep North Atlantic. Except for the Kirov and SSNs, I don't think too many other nuclear powered ships were lost.
Off the top of my head, there were actually quite a few nuclear subs lost in the war, in addition to the Victor III sunk near the
Doria.
Pharris was involved in the sinkings of a November & a Charlie-II both in the mid-Atlantic.
The British frigate captain mentioned that HMS
Diomede sank an Echo-II somewhere in the North Atlantic in a conversation with Ed Morris. A number of Soviet subs were sunk trying to go after the amphib group that retook Iceland, some pretty close inshore, including a Victor, a Papa, and an Oscar.
In the briefing for Operation Doolittle, it's mentioned that HMS
Trafalgar was sunk by a mine in a shallow part of the Barents or Norwegian Sea.
In the running battle that the attempt of the US subs that launched the TLAM strike to flee the area resulted in, several Soviet subs were sunk, apparently including a Victor-III or two. Finally, in the penultimate sub battle, an Alfa as well as
Boston & Providence are all lost.
Although nothing more specific about nuclear sub losses is mentioned, in the Soviet leadership scenes, it's mentioned that Soviet sub losses are very high. Nothing else is mentioned about NATO sub losses.
Nothing's mentioned about any US nuclear carriers or cruisers being sunk.
These subs certainly would be an ongoing environmental concern. So far, there hasn't been any leakage from the reactor vessels of
Thresher or
Scorpion, both of which have been on the bottom for over 40 years. Less is known about the reactors of Soviet subs that sank OTL, or those that the Soviets and post-1991 Russians simply dumped in the Barents Sea a hundred miles or so off Murmansk, including the scuttling of several boats that became damaged and contaminated beyond repair as the result of reactor accidents, in contravention of international treaties.
In the RSR TL, the Victor sunk next to the
Doria would be a major concern, as the depth charges that sank it caused a reactor accident- some sort of uncontrolled event, and its implied that the explosions may have breached the containment vessel.
AFAIK, the
Bellona Foundation might have more info on these subs and the dangers they could pose. (OTL, not in the RSR TL), as IIRC, the subs & reactors dumped at sea by the Soviet & Russian Northern Fleet is one of their ongoing projects.