I've seen this from several sources, that when the war started turning against them, the Nazis accelerated the killing.

First, is this true, and second, why? The infrastructure and manpower required to exterminate a race isn't exactly a line item. That's a huge amount of effort and planning and logistics and people and ... moving parts, that all could probably have been better spent trying not to lose the war.

I've seen some explanations (that I perhaps just didn't really grok) that the leadership believed that it was the Jews who were (perhaps just 'behind') the opposing sides in the war, and that if they just managed to kill all of them... What? The war would end? Victory?

That seems... irrational. I can buy that someone thought that, maybe even a few people, but surely there was someone in Nazi leadership who realized that was completely stupid?

Was this some insane sacrifice? Like, we'll all die, but if we manage to take down the entirety of the jewish race with us, the survivors will be able to complete our grand destiny?

Was someone trying to "hide the evidence" of the holocaust by killing all the witnesses?

What was the thinking behind diverting resources away from the war, towards killing a lot people who were not a threat?