Native Americans make up 5% of the AZ population and 12% of the Covid deaths. That's disproportionately high, but doesn't really explain the higher death rate in AZ - its a (minor) factor.
Most of the public HS that kids on my son's team went to were closed for a large portion of the school year. Charter & private schools followed their own paths, excluding a few weeks at the start of the school year as you said. Most every school, that I'm aware of also had an online learning option and so followed a hybrid model with mask mandates in school.
Fwiw, I do think AZ has handled it better than CA, and I'm happy about that.
any unified theory of what happened in Arizona has to account for what happened in New Mexico as well. New Mexico did relatively well compared to Arizona but it's lockdowns were as harsh as California and they had a limited travel ban in place plus New Mexico (unlike Texas, AZ, and California) isn't really a surge zone for southern border crossings due to the location of its cities. Relative to California (with it's SoCal variant) or even neighboring Colorado (which pursued a much more moderate policy) it's not a good outcome.