Unless one more pronge of attack is launched through Ulanqab-UlaanBaatar direction. In this case, logistics allows Japanese to just reach Baikal within 6 months. That pronge was not considered IOTL due expected heavy Soviet-Mongolian field fortifications, which were actually very poorly equipped after Barbarossa started.
An attack in this direction was included in Hachi-Go Concept B (otsu), which was the plan developed in 1938 for a hypothetical war in 1943. But, it appeared in neither the war plan of 1940 or in Kantokuen, which was inspired by the 1940 plan. After reviewing Hachi-Go's "otsu" variant, the Army General Staff concluded that such an undertaking would require 200,000 trucks - double the number that were in the IJA at any given time. Furthermore, the results of the Battle of Khalkhin Gol (Nomonhan Incident) discouraged planners from contemplating large sweeping movements through endless tracts of steppe and desert, which as a rule were devoid of any infrastructure. The logic is easy to see: the distance from the eastern border of Manchuria across Primorye to the Pacific Ocean is about 230 to 330 km, from Baotou to Ulan-Ude nearly 1,300 km.
In any case, the strongest defenses on the Western Front were the Dauriya and Borzya Fortified Regions, not southern Mongolia.
The condition "Soviets became so badly weakened from the war against Germany" was true. Regular Siberian divisions were in the process of removal in middle August 1941 (with about 50% of forces already departed, and remainder stripped of most effective war equipment), leaving poorly equipped (i.e. only artillery was immobile coastal artillery), manned by substandard (over-aged) personnel, and barely trained replacements. Japanese just have failed to get enough spy data to understand how much Soviet forces in region were weakened.
Without the second stage of the Kantokuen buildup (up to 25 divisions from 16), the Kwantung and Korea Armies did not possess the ability to conquer the Soviet Far East. In the opinion of the Kwantung Army, 'to crush the Soviets with such a small force' (760,000 in Manchuria and 120,000 in Korea) was "absolutely impossible." According to Yutaka Imaoka, one of the leading logistics experts in the IJA, operational planners were speaking in terms of 1,200,000 men in 23 or 24 divisions, supported by 35,000 trucks, 500 tanks, and 400,000 horses on the eastern and northern directions alone (that is, excluding Mongolia, Sakhalin, and Kamchatka). Additionally, between 2,100 and 3,100 aircraft, including 350 belonging to the Navy, were expected to take part.
As for the Soviet Union, although the quality of personnel and level of equipment declined significantly compared to early 1941, manpower actually expanded as the Red Army moved to full wartime mobilization. For example, although the number of personnel in the Far Eastern Front and Trans-Baikal Military District was only 651,000 as of 1 June 1941, by 20 December there were more than 1,161,000, including 30,000 trainees.
By comparison, the Japanese estimate of Red Army strength at this time (800,000) was short by more than 300,000 people. Estimates of Soviet tanks and airplanes in-theater were even more off the mark, though the point must be made that their figures refer only to vehicles in operational units, not in reserve or otherwise inactive.
Category.........................................................
Soviet figures..............
Japanese Intelligence Estimate
Army (excluding Navy, NKVD, Mongols)........... 1,161,000.................. 800,000
Tanks and SP Guns........................................... 2,100........................ 1,000
Aircraft............................................................. 3,100........................ 1,000
Warships.......................................................... 96 ............................ 105
* Approximately 660 tanks and 347 aircraft were inoperable at the beginning of 1941, these numbers may have increased post-Barbarossa owing to demands for spare parts.
Especially in Primorye, Soviet defenses were situated in parallel belts dotted by hardened fighting points. In most cases these were mutually-supporting and well-sited on the avenues of approach over the frontier; only concerted attack by heavy artillery, aircraft, and finally close infantry assault could overcome them. The Soviet border was probably better fortified in 1941 than the Manchurian border was in 1945, where the Kwantung Army's defensive points were more like "islands" than a continuous "Maginot Line."
This is not to say that Japan couldn't win at all: by factors of geography and certain military realities expanded upon below the Russians would have been doomed. But, it would not have been easy, and without the full-bore commitment authorized by Hirohito on July 7th - practically impossible.
Since the Japanese cannot go north and south at the same time, let's presuppose they have the oil and other raw materials they need to keep the war in China going on some level and attack the USSR sometime after Barbarossa kicks off. Let's also assume they wait until Siberian forces and equipment have moved west leaving the east relatively weak. Japanese armor sucks compared to what the USSR has, and their logistics are poor. I would say their army and naval air forces are better than what the Soviets have especially in the east. There is no comparison between the IJN and such Soviet naval forces in the Pacific. Then trans-Siberian RR represents a real vulnerability for the USSR, limited capacity even if not under attack and has multiple places where interdiction would be a real problem.
It was all the USSR could do to deal with a one front war in spite of the many German "failures" such as logistic planning when Barbarossa kicked off. Even if you assume no Soviet forces were sent east to deal with Japan, they still need to provide ammunition and fuel well above what was used 1941/42 in the east when things were at "peace". every bullet or gallon of fuel used in Siberia is not being used against Germany. I can see the USSR conceding everything east of Baikal for sure, fighting as hard as possible but simply deciding that they can do without the far east better than they can do without Moscow or Leningrad because resources were sent east.
Despite their size, the Soviet forces were qualitatively far below the Kwantung Army on a unit-for-unit basis at that time; they weren't as well trained, had poorer officers, lacked the same fanatic motivation, and weren't as physically fit for duty. Because of a lack of operable vehicles they were virtually immobile and could not conduct any long-distance movements. The positioning of the Red Army in a gigantic semicircle around Manchuria also provided the Japanese with an excellent opportunity to destroy it piecemeal.
Worst of all though was the remoteness of the Far East from European Russia, and, as you said, its dependence on the single Trans-Siberian railroad. Without that railroad, the isolation of Soviet forces from the "center" would be complete, and neither they nor the region as a whole had any hope of offering large-scale protracted resistance because they were not self-sufficient in either food or raw materials. (In any case, the only reinforcements promised to the Far Eastern and Trans-Baikal Fronts amounted to five artillery regiments, six guards mortar regiments, and five armored train divisions altogether.)
In light of all this, Soviet operational planning was "damned if you do, damned if you don't." On the Eastern Front, STAVKA's Directive No. 170419 (15 March 1942) actually called for a counteroffensive along both sides of the Sungari River to protect the regional HQ at Khabarovsk, which was right across from the Manchu border. Smaller-scale attacks "in the tactical depth" were to be made elsewhere as official policy called for all-resistance in the border region with little consideration for defense in depth. This would have been a viable strategy if the Soviet command possessed a real mobile reserve, but they had none: the various armored units were scattered willy-nilly among the infantry and at any rate had little ability to maneuver coherently outside their area of deployment.
The outcome would have been that once any given part of the defensive "crust" was breached, the entire front would have crumbled - an effect exacerbated by wasteful counter-attacks similar to what was seen in Europe. Past the initial stages of the war, the Soviets also would have had no answer for the Japanese Navy, Air Force, or WMDs, the latter being especially devastating against food sources and populated areas. To this end, three major 'detachments' of the Japanese Army - Unit 731, Unit 516, and Unit 100 - began studying the most effective way to facilitate ground operations, and "epizootic detachments" were organized at each corps-level headquarters to increase readiness for biological warfare.
