Russia looked at nuclear batteries when their AIP efforts for Lada/Amur hit a dead end. But nothing came of that either. As for a full on reactor, I suspect the complexities and cost of design and operation will quickly approach the level of SSNs, hence why the entire effort renders itself somewhat academic. My personal guess is China will for some time continue modernisation of SSK forces incl AIP, but at the same time increasingly focus on a nuclear powered fleet for their most relevant assignments.
Or Russian special purpose nuclear subs.
Although I have my doubts on "comparable noise levels to conventionally-powered SSKs". Natural circulation?
You should learn about its civilian prototype: the 5MW Nuclear Heating Reactor (NHR-5) built in the 1990s.This type of reactor is superior to Canadian AMPS.The only information we have on the "mini-nuke" right now can be summed-up as "basically swapping the conventional propulsion system on SSKs with a small-sized nuclear reactor":
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According to the slide, the SS(N)Ks should have "unlimited endurance after just one fuel-up" and "comparable noise levels to conventionally-powered SSKs".
The closest model resembling the SS(N)K (in terms of displacement and propulsion) would be the Rubis-class SSNs of the French Navy.