Genuine question: Do we have data that collaborates the theory that AC's prevent heat deaths and it's not due to confounding variables like the air in Nevada being dryer (dry heat is more bearable than wet heat) or the people in Nevada having year round higher temperatures and just being more acclimated?

Has been on my "to research" list for a while. I agree with you that Europeans should stop being so stingy with AC (speaking as an European who still hasn't an AC, but not much longer), but I do wonder how much they actually do to prevent heat deaths.

Because, how many heat deaths happen at home where people would potentially have AC? As far as I can tell (pre researching it) most, if not all, heat deaths I am aware of, happen outside. So the question would be: What is the effect of having a cool 22C home in regards to suffering heat deaths outside. Does it make it better, because your body can cool down? Does it maybe make it worse, because you step into a harsh difference when leaving it? (The last one is probably an easy no, since plenty of countries with high AC rate don't seem to have that issue).

(Or just general damages from heat, not just heat deaths)

Exactly. The recent heat deaths I saw were people getting heart attack from jumping into cold river and others mostly from dehydration. All are from outside.

You will not die from sleeping in 30c. What europe will have to get used to is slow down over the mid day when the heat is worst.