In that case we can conclusively say it was an utter failure. The Germans successfully rerouted their forces and launched Operation Barbarossa, the largest and most successful military operation in human history.

You can't directly compare an air battle and a land battle in terms of casualties.

What the Battle of Britain did is twofold.

1) It kept open another front which prevented the Germans from throwing their full weight against Russia

2) It guaranteed air supremacy for the allies (and especially the RAF) for the rest of the war. Not having air supremacy is an absolutley crippling disadvantage.

1. The forces reserved for Operation Sea Lion (the planned amphibious invasion of Britain) were successfully rerouted and deployed as part of Operation Barbarossa. Hence, the Battle of Britain completely failed to prevent this.

2. This may be true but it doesn't change the fact that the Axis was crushed almost entirely by the Soviets with comparatively little being accomplished by the British.

Fun fact: More Axis aircraft were lost in the highly successful Operation Barbarossa than during the entire Battle of Britain. Once you factor in the Axis aircraft lost during the continued fighting on the Eastern Front and it's really quite one-sided. This doesn't even take into account the nearly 10 million Axis casualties inflicted by the Soviets. Over 90% of all Axis losses can be attributed to the Soviet Union. The USSR technically dealt approximately ten times as much damage to the Axis as all other Allied nations combined.

Which was doomed from the outset and opposed by many people in the German military. Just because they did it didn't mean it was logical or a good idea. Holding off the Germans in the Battle of Britain didn't stretch the Germans intially because the Allies didn't return with aggression; they simply weren't ready. But by 1943 when the bombs started dropping and in 1944 when invasion was imminent, it was the death blow to the Nazis. They simply couldn't handle both the Russians and a coordinated Allied invasion from the west. Without Britain, that simply wouldn't have been possible.

It's not a resource thing, it's about the arrest of momentum. Those 3700 people were enough to convince Germany to stop trying on that side, which left the Western Allies breathing room and a handy base of operations

I find it a little difficult to swallow that the Soviets singled-handedly crushed the entirety of the Axis powers when they fought neither Italy nor Japan in force. Italy was almost a laughing stock, for sure... Japan, not so much.

Threat of the Soviet Union (despite their nonagression pact) did hurt the Japanese war effort, as they had significant resources invested in Manchuria awaiting the invasion, which could have been used to build control over the Aleutians or make the difference on Guadalcanal.

They distracted the Japanese, yes. But distraction without major conflict is not the same thing as actually defeating the enemy.

Britain didn't contribute anything meaningful to the Front with Japan either so what's your point? Although it is worth mentioning that the Soviet invasion of Manchuria saw the Soviets killing or capturing over 700,000 Japanese troops. Also, Romania, Italy, Hungary, Slovakia and Spain all contributed to the Eastern Front. The Italians lost almost all of the 100,000 troops that they provided for the Siege of Stalingrad alone. If you factor in Manchuria the Soviets inflicted over 10.6 million casualties upon the Axis, again, more than all other Allies combined.

The Soviets invaded Manchuria after America had dropped two nuclear devices on the home island. They were picking up scraps and trying to grab land, nothing more.