It is a great question. In my experience it is hit or miss. Haier advertises all auto restart in their products. The little ones on amazon use a peltier action so no compressor. If it has a physical switch it turns back on. When there is a compressor it is more complicated. I think it would need a secondary controller. Otherwise it can’t overcome an interruption. That’s the regular consumer stuff for sale now.

There were some brands like active air and environmental controls. They made those controllers and relays for powerful equipment.

Hopefully somebody who knows more than me will chime in. I wanna know more.

A creative electrician could make a ‘Wake the fuck back up’ relay circuit. It would need a timer, micro controller and a capacitor. I’ll bet they make things like that for servers and computers. It must exist.