These kind of “manual” a/c units normally have a little sticker or a caution in the manual to “wait 5 minutes before restarting”.
People can easily trigger this kind of thing just by turning the thermostat back and forth, so there is usually a thermal cutout on the compressor to keep them mostly safe.
You can usually hear it when it activates, there will be a hum from the stalled compressor for a few seconds and then a little click, and then the compressor won’t start for a minute or two.
Everything is fine in the Apple ecosystem as long as you want to do something The Apple Way™.
As soon as you want to do something differently to how Apple decrees it should be done, then you’re screwed.