Would Russia assert itself in this theater in the middle 1880s though? The Trans-Siberian was as yet, just a dream. Russia seemed to be more concerned about Bulgaria, Afghanistan and the British Raj than the Far East.
Might the Franco-Japanese connection make Russia think even harder about pushing Japan around at this time? Perhaps into thinking that the better course is to pile on China.
When Russia wanted southern Sakhalin a decade earlier it treated Japan as an equal, trading the Kuriles to get Sakhalin. If Russia had thought Japan was a pushover, Russia would have been all take and no give instead.
https://en.wikipedia.org/wiki/Treaty_of_Saint_Petersburg_(1875)
I think there would be several concerns for Russia that would push it to intervene in Korea in the event of Japanese intervention:
1) Russia in 1884 actually did have the resources to intervene against Japan, having received reinforcements in a rush to upgrade its capabilities following the Ili Crisis in Xinjiang of 1877-1881.
2) It is unlikely that Russia would intervene against China over Korea:
a) there was a healthy (maybe exaggerated) respect for the Chinese military during this period, with intel estimating the Chinese having around 260k modern rifles + artillery in Manchuria.
b) Britain had intervened in favor of preserving China's territorial integrity during Ili and would likely do so again in response to Russian moves against China (which would inevitably involve Xinjiang).
c) Russia would have known through diplomatic channels that Li Hongzhang was uninterested in pushing back Russia in Central Asia (to the extent that he even thought of conceding not just Ili, but Xinjiang to Russia), so why undermine his position and assist the rise of hawks?
3) Russia thought Japan was a pushover and the only reason it dealt with it in the 1870s because it feared a Japanese-Chinese alliance aimed against it in Manchuria. Even on the eve of the Russo-Japanese War the Russians held outlandish views about Japan's military capability like 'Japan lacks the moral base to match Europeans' (Vannovskii, in charge of Japanese intel) and that 'Japan was too atheist for war' (Kuropatkin, War Minister).
So in this scenario:
1) If Russia intervenes against China in conjunction with Japan + France, it
might gain something (probably in Central Asia rather than Korea) but it would
certainly bring on British intervention and Chinese antagonism, which was not worth it at all; and
2) if Japan makes gains in Korea, Russia would feel itself completely capable of intervening against Japan - not war, but pressured negotiations in order to guarantee Russian interests in Korea.
Ultimately, Russia (or at least the parts of Russia interested in the Far East) wanted to build up strength in the region until it could erode the Chinese periphery further (esp. Inner Manchuria), and for that it desired a static regional situation, hence the grudging acknowledgement of the Chinese position in Korea.