If the Japanese attacked
What would have happened if the Japanese had attacked the Soviets in the fall of 1941 or the spring of 1942? Well, to make such an attack plausible the US would have had to refrained from imposing the oil embargo on Japan. That's not too implausible. The Roosevelt administration could easily have figured that putting the Japanese in a fight or surrender situation at a time when the US could have really used another year to rearm and the British already had their hands full elsewhere wasn't too smart.
So the US doesn't impose the oil embargo--at least not yet. At that point the Japanese are divided between a "Go South" faction that is primarily though not exclusively Navy-based, and a "Go North" faction that contains some but not all of the army. Both factions see the potential for easy victories. Neither faction can realistically hope to defeat the opponents that their plans will bring into the war, but as the attack on the US proved, Japanese foreign policy in late 1941 wasn't realistic.
So, in late summer of 1941 the "Go North" faction wins out. The Japanese have already been building up in Manchuria. They accelerate the build-up. Historically they created 3 armored divisions in Manchuria in March of 1942 if I recall correctly. I don't know if they could push the formation of those divisions forward into late 1941. In any case, they wouldn't be particularly powerful divisions. The main tanks would be an outdated light tank with 37 mm main gun and a pretty decent medium tank that suffered from having a low-velocity 57mm gun. They were planning to upgrade the medium to a higher velocity 47 mm that would have been effective against most Soviet tanks of the era, though I wouldn't want to try that out against a KV1. I don't know if any of the upgraded tanks had been fielded by the time-period in question.
Presumably the Germans would have had the same initial successes against the Soviets that they did historically. The Soviet spy-ring inside the Japanese government would let them know that, yes the Japanese will be coming north. Does that have any impact on the fighting against Germany in 1941? To some extent. The Soviets did pull a few divisions from the Far East over the course of Autumn 1941, and more in the winter, though the extent of that shift has often been exaggerated.
Having the Japanese as probable active enemies would rob the Soviets of a few experienced divisions in the fall of 1941 and a few more in the winter of 1941-42. It would also put more stresses on their ability to supply their armies with ammunition, spare parts, and trained specialists--including pilots. War stocks in the east would have to be maintained and added to, rather than being available as a reserve. How much impact would that have in the fight against the Germans? My guess is that it wouldn't make a whole lot of difference, but I would have to look at the details before I could say that for sure.
So the Japanese enter the fight, maybe in September/October 1941. Not a pleasant time to be fighting in Siberia. Maybe they wait until the spring of 1942. In any case, how would that go?
We have two clashes between the Japanese and the Soviets to give us some indication of their relative strengths. The Soviet seizure of Manchuria at the end of World War II was impressive, but it came after four years of learning how to do armored warfare at a time when the Japanese had pulled many of their best troops out of Manchuria to fight elsewhere and starved their army of equipment to keep the navy in the fight against the US. It doesn't tell us much about how the Soviets would have done against the Japanese in late 1941/early 1942.
The battle of Nomanhan in the summer of 1939 tells us some things, but the Soviets had a much larger number of divisions (at least 5 and possibly 7--I'll have to check) against one inexperienced Japanese division and elements of a second one--at least 3 to 1 odds and even greater odds in terms of firepower and tanks. In addition, the Japanese command back in Tokyo worked hard to prevent the Nomanhan fighting from becoming another open-ended adventure like the "China Incident". That meant that the Japanese made it clear that they would not escalate to other parts of the border and for the most part they kept their airforce from raiding outside the immediate area of the fighting.
The Nomanhan fighting did show some things: The Soviets had better firepower, better tanks, and knew how to use them better. Ironically, even after Nomanhan the Soviets broke up their large armored formations for internal political reasons and then hastily reformed them too late in the game for them to regain their effectiveness in the early fighting against the Germans.
The Japanese showed some good and bad traits. They had gotten sloppy against poorly-armed Chinese armies, and that cost them. At the same time, they were tough aggressive fanatical fighters. Nomanhan was not a cakewalk for the Soviets. Casualty figures for the battle are still kind of murky even after all of these years, but as near as I can figure the Soviets lost almost as many men killed or wounded as the Japanese did--that when the Japanese division was enveloped and defeated in detail. The Japanese were already displaying the fanaticism that they showed later in the war, with officers sending "human bullets" out to knock out Soviet tanks--with a surprising amount of success in the early going.
The Japanese would probably quickly establish air superiority if they went up against the Soviets. They would eventually lose it if the Soviets survived.
The Japanese would obviously have naval superiority as long as the US didn't enter the war, cutting off Lend Lease to the Soviets from the Pacific side. That wouldn't have much impact in the early going, but would pinch if the war lasted into 1943-45. Without as much Lend Lease, the Soviets would have had to produce more trucks and fewer light tanks. They would have had tighter food rations, less aviation fuel, less synthetic rubber, etc.
On land, the Japanese would have had a constant fight to keep their tanks and artillery competitive. If they stayed out of war with the US, they would have been able to concentrate production on tanks and artillery as opposed to ships, which would have meant that better designs made it to the battlefield in larger numbers. At the same time, they would have had major problems in 1942 if the Soviets sent even a few hundred T34s and KV1s to the eastern front. Going up against a KV1 with a Shinhoto Chi-Ha or a Chi He if it had gone into production would have been an act of extreme bravery.
One thing to keep in mind: the Japanese had been fighting in China since 1937, and building a navy far too big for their economy. They would have probably run out of money for imports sometime in 1942 unless they were able to seize valuable commodities from the Soviets and find a market for them.
So: no definitive conclusions, but hopefully some insights into some of the constraints both sides would have had to deal with.