How To Handle Power Outages With Remote Macs?

At my condo, which I visit monthly, I have a 2010 MBA (High Sierra?) that runs a webcam and performs various other periodic tasks. I don't have an UPS for it, but the internal battery usually lasts long enough to handle power outages. However, this week the condo scheduled an all-day outage in order to do maintenance on the electrical systems. I have the MBA scheduled to "Start up or wake" every morning. (This MBA does not have "Start up automatically after a power failure".) As expected, the MBA's battery went dead during the power outage. I expected that the battery would charge up after power was resumed and that the MBA would start up on schedule. It did not and remains shut off.

What should I have done differently?

At home I have a 2017 iMac running Catalina. It has a UPS with a battery that lasts about an hour after a power outage. When the battery gets low, the UPS sends a shutdown command to the Mac. During a long outage the UPS shuts the Mac down and then turns itself off when the battery dies. When power resumes, the Mac starts up automatically. ("Start up automatically after a power failure" is enabled.)

However, this week, while I was away, there was a power outage. The outage lasted long enough for the UPS to shut down the Mac, but power resumed before the UPS shut itself off. So, power to the Mac was never lost. As a result, it stayed shut down and required manual intervention to start up.

What should I have done differently?

You might want to consider replacing the MBA with a Mac Mini, perhaps a previously owned model from OWC which as some real inexpensive models. Your needs don't seem to require a superlative machine with lots of RAM & etc. The Mini should be able to provide the startup after power failure option because it is a desktop Mac.

For the problem of starting up the iMac in the circumstances you described, you should consider creating a series of Terminal pmset commands which wakes or restarts your Mac with a frequency you find amenable.

This example should attempt to wake from sleep or power on the Mac on an hourly basis every day:

pmset repeat wakeorpoweron MTWRFSU 01:00:00
pmset repeat wakeorpoweron MTWRFSU 02:00:00
pmset repeat wakeorpoweron MTWRFSU 03:00:00
.
.
.
pmset repeat wakeorpoweron MTWRFSU 24:00:00

If the Mac is already up and running, these commands have no effect. A wealth of information is found in man pmset.

The app Power Manager may also be helpful as it provides a GUI method for setting the same commands.

_{Disclaimer: I have no financial or other ties to the developers of Power Manager, nor in Other World Computing, Inc.}