I know this is an extreme oversimplification, considering the many complex facets (weather, air-power, artillery, leadership, strategy..) but how significant was the T-34 also from the Germans perspective?
I do not think you could make a convincing argument that the T34 on its own was the single largest factor to soviet success on the eastern front due to a number of things you already listed. Although I can talk about at length the significance of the tank its impact.
The T34 was an important introduction in soviet armor because it combined a variety of great qualities that made it an essential part of the soviet arsenal. It was a relatively simple machine to build, using simple welding techniques, materials, and methods of production that allowed it to be rolled out en masse from refitted Soviet factories beyond the Urals. There's even a famous anecdote from Stalingrad that the massive Tractor Factory was still refitting and rolling out T34's while the 6th Army was directly assaulting the industrial north of the city in the autumn of 1942. tens of thousands would be produced in factories all across the soviet union during the war, and would go through different modifications such as modifying the turret to change the model to the T34-85, which had an 85mm gun instead of the lower caliber 76mm main gun. The commander also could focus on commanding the crew instead of having to function as the gunner at the same time as was the case in the older model. The newer modifications were heavier, but they were more effective against upgunned Panzer MkIV's and newer Tiger, and Panther models that they began to encounter in late 1942 and mid 1943 - most notably at Kursk.
The T34 was more reliable than their German counterparts due to a number of reasons. The T34 used a robust diesel engine that provided ample power with a lesser degree of maintenance and care required to keep it running. But early models suffered terrible teething problems with their tracks, their radios (if the tank was even fortunate enough to have on), and their transmission - their Turret drive also was unreliable when they were first introduced. This made many believe that German tanks were at least initially more reliable than their Russian counterparts, but it would prove later to be the opposite as the various problems encountered were more or less remedied with field or factory modifications.
Another factor in the T34's impact was its very wide tracked and reliable suspension that afforded it great mobility even on some of the most treacherous roads in Russia. German tanks and other vehicles had thinner tracked set ups and less robust suspension that made them more liable to stoppages and other issues regarding mobility when they encountered phenomena like the infamous rasputitsa - the rainy season or annual thaw of the hard winter ice. The T34 was much better suited for traversing the roads during this time, but even they could get bogged down or slowed substantially by weather.
While its armor wasn't necessarily the thickest with later models having 20 to 90mm's of armor at most it made up for this deficiency with an interesting solution. By sloping the armor it could in theory double the amount of distance a round has to penetrate if it is fired directly towards the frontal or side armor. as this illustration points out. So even with thinner armor than heavier German tanks, the T34's were extremely difficult for the Germans to disable. Earlier Panzer Mk III's and IV's had smaller caliber and lower velocity guns that could not penetrate the T34's sloped armor, with many rounds simply bouncing off. The Germans had similar troubles with the heavier KV1 and KV2 model tanks that had very thick armor. The Germans often had to rely on the 88mm anti aircraft gun to disable T34 or KV2 tanks because of a lack of heavier and higher velocity tank guns like the 7.5cm Pak 40. This caused significant problems for tank formations that could be ground to a halt by the appearance of T34 and KV2 groups. Upgrades to German tanks and introduction of superior models would remedy this, but they could never match the production numbers of the ubiquitous T34.
Soviet Tank and Deep Battle doctrine also created a unique organizational structure for tank formations in the creation of Tank Armies solely comprised of tank corps that could often be supported by squadrons of IL2 Sturmovik attack aircraft. As the war progressed and the tactical planning and operational effectiveness of Red Army commanders increased there was increased cooperation between tank armies, shock armies, aviation armies, and artillery that rivaled German Blitzkrieg and Schwerpunkt tactics. Shock armies would probe and bust open holes in German lines that would quickly be exploited by extremely mobile tank armies thrusting deeper and deeper behind enemy lines to cause chaos and prevent them from offensive maneuvers. This was used to great effect in Operation Uranus (surrounding of the 6th army in Stalingrad) and Operation Bagration (the destruction of Army Group Center and the retaking of Belorussia).
The T34 had a significant impact in the Eastern front through its ease of production, simple yet effective armor, robust suspension, and good general armament. But the T34 was useless on its own without proper air, ground, and artillery support along with tactical and operational planning that exploited its abilities to the fullest. The T34 was a brilliant instrument of war, but it was only one tool in a massive arsenal that required a great deal of staff work and leadership to utilize properly
Sources: Anthony Beevors Stalingrad, Richard J. Evans Third Reich series, various documentaries I've seen over the years like Battlefield, T34 wiki mostly for numbers and other information
German tankers noted:
“T34s operated in a disorganised fashion with little coordination, or else tended to clump together like a hen with its chicks. Individual tank commanders lacked situational awareness due to the poor provision of vision devices and preoccupation with gunnery duties. A tank platoon would seldom be capable of engaging three separate targets, but would tend to focus on a single target selected by the platoon leader. As a result T-34 platoons lost the greater firepower of three independently operating tanks."
The T-34 looks great on paper, but is a severely flawed design. The tank's commander, gunner (and possibly platoon commander) were the same person. Combined with weak optics, a cramped turret, often operating without a radio, no turret cupola, no turret basket, and only one periscope for the tank commander, the T-34 was often slow to find and shoot at targets, and lacked the ability to engage separate targets.
T-34 losses in 1941 were considerable (some 2,000+) and while some were operational losses, many were not. When you consider this was against tanks and anti-tank guns often labelled as obsolete or obsolescent, you have to raise an eyebrow. In 1942, 6,000+ were lost, and many of those cannot be attributable to operational causes; the vast majority of them fell to enemy action. In 1943, 14,000+ were lost, the vast majority to enemy fire. In 1944, another 12,000.
While strategically important thanks to its ease of manufacture and simple design, don't confuse it with being worth a damn in a battle.
A very good intelligence assessment of the T-34 here, by the way it does not live up to the expectations.
