My plans went awry. I leave Sat, with (God willing) the last details to be finished tomorrow. I dug out Alvin D. Coox's "Nomonhan: Japan Against Russia,1939, and got some of the details needed.
With the start of the incident, and its growing escalation, will this butterfly the Finnish War? How will the Purges be affected? That's for you as the author to decide. In OTL in 1945, the a large part of the Soviet Advance into Manchuria came out of Mongolia. As you said, this will (in 1939/1940) be with cavalry units. At this time, the IJA isn't too deeply mired in China. They have the troops to make a good fight with the Soviets. Their problem is that they are very, very weak in armored forces, and not nearly as well equipped as the Soviets in artillery and anti-tank weaponry. The Japanese have learned this, after the Red Army curb stomped them quite handily. This is a quote from the book. "Two years after the experience at Nomonhan, IJA ground divisions were still markedly inferior to Red Army divisions with respect to firepower, mobility, armor, and air support." (Coox, p1052) This means the IJA troops badly need difficult terrain to make their stands. IMO the Soviets will push them further and further back towards Harbin, which they will make a great effort to save. Much will depend on how much time and effort Stalin wants to put into this at this time. Whatever his shortcomings, he was no fool, and won't be entirely comfortable with keeping too many troops in Manchuria when the Germans have taken half of Poland. On the other hand, he may decide to clear up the situation in the East by beating the hell out of the Japanese so he can concentrate on the looming German threat.
If Stalin goes all in, he will push the IJA out of Harbin and back southward. I can see a lot of the IJA troops from south of the Great Wall and Peking being transferred, and possibly, if the situation grows dire enough, the Japanese opening negotiations with Chiang Kai Shek and the Japanese pulling out of Northern China entirely. Japanese industry is not going to be able to meet the demands of the Army in time. This will force the Japanese further and further back into the mountains, where their limited weaponry is not at such a disadvantage, and nullifying the Soviet advantage in armor. This was, in fact, the plan for 1945. The "Redoubt" was to run from Ant'u in the north, to Tonghua in the center, and finally Liaoyang in the south, using the terrain of the Changbai Mountains. (Page 1064). I'd expect successive lines of defense going back to and behind the Yalu River.
This is a good scenario for a TL. It opens several possibilities. Will Germany defend against France and England, and attack Russia early, while they are heavily engaged in Manchuria? How far will Stalin order the Red Army to go? Will Chiang Kai Shek make peace, so he can destroy the Communists? Kudos to you for bringing this one up!
As to the IJN, an enlarged war in Manchuria will butterfly away further Japanese advances into China. No embargoes, no "Southern Strategy", no Great Pacific War. The IJN may try, if they can get sufficient troops from the Army, to take Kamchatka, but that's just off the top of my head, so don't put too much credence to it. All in all, the IJN will continue to be a modern navy, but probably smaller and less relevant. The Army will be needing better equipment, and with no likely maritime enemy, the Army will grow, while the IJN wont.