Well, if they destroy the Japanese Navy, resupply becomes rather easy- as does looting Korea for a lot of goodies
Oh sure... like the Koreans would happily let the Russians strip their country like the Japanese did IOTL.
And with
what ships? Russians don't have nearly enough troop ships and supply ships (i.e. nil), nor the port capacity in any of its nearby ports to support an amphibious operation on Japan. They can't just magically teleport their troops onto Japan, or freeze a bridge across the Sea of Okhotsk and march across.
If they tried a landing, their landing party will be limited by how many troops and supplies they can carry on their ships, and they'll be expected to hold in hostile territory before they can get reinforcements. Any force too small would be destroyed and its survivors marched off to prison camps before any relief comes along. As Cueg stated, 'anything less (than 200,000 men) would be destroyed'.
The Royal Navy? Now that is an interesting question
In a Russian victory scenario the Russians would have 15 relatively modern battleships in the Pacific and have demonstrated that their navy is tactically and technically capable
For Britain, a defeat at Sea means the end of her Empire, the destruction of her economy and the possibility of foreign occupation. That's a lot to risk. To do so, the British are going to have to feel that absolute vital interests are at stake and send a force that will win decisively- a victory where the British lose a bunch of battleships is devestating- infact its exactly what Tirpitz planned all along
So figure the British would need a 2-1 advantage over the Russians or 30 Battleships. Are they really going to deploy that much to protect Japan knowing that it opens up their Islands to attack from France or Germany?
A defeated Japan isn't worth that much to the British- the likely scenario is that Britain shops for allies (the US) and doesn't get any help. Roosevelt would do it but the Congress wouldn't let him. The Germans certainly aren't risking Berlin for Tokyo-something they had made rather clear
Once that failed, the British would be stuck trying to negotiate directly with the Russians. The entente with much more favorable terms to Russia is the most likely
Japan isn't totally wrecked (their Home Islands are still intact), and the British won't allow the Russians to do too much damage to them. And unlike Russia, Britain places more emphasis on its navy to maintain its colonial empire, and is rightly cowed when facing a land-based battle during the Great Game in Afghanistan. Same case for the Russians when facing off against the British at sea. A total fall of Japan, if that were ever possible, would spell doom for British naval interests in the Pacific. And they have little to fear when dealing with two disparate Russian navies that had to play second fiddle to the army.
Did I mention they have the Suez too? If the Russians even attempt to meet the Baltic and Pacific navies together, they'll have to pass through the Cape of Good Hope, across entire continents of hostile coast and with the gleaming possibility of the RN simply taking the shortcut to wreck them one by one, with the luxury of supply from any port they own along the way. And there are
many.
But I digress. A Russian invasion of Japan at this stage is ridiculous. It would have been better for Russia to settle for a favourable peace without trying to invade the Home Islands, which would be a lot more possible.