Error doing restore/revive via Finder

Make sure you are using a USB USB-C cable such as the Apple USB-C charging cable which shipped with most Apple Intel Macs. You must connect this USB-C USB-only cable directly to the back left USB-C port on the M1 MBAir as well. An Apple Thunderbolt3/4 cable will not work for this process.

I would connect the power adapter to the laptop as well.

Did you see the "DFU" symbol/notice on the screen which confirms the laptop was in DFU mode? If so and the process failed, then it most likely indicates a hardware issue with the Logic Board. You can try the process a couple of times just to be sure it won't complete. If you do not see "DFU" listed, then the Mac is not in DFU Mode. I believe the Finder method of performing this "Revive" or "Restore" will show "DFU" when the Mac is in it. I don't know if it will tell you any other status information in case the Mac is booted normally, but has no video on the display. The Apple Configurator option does mention if the Mac is in some other state (may not tell you what that state is, but you know it is powered on & not in DFU mode).

You can try to reinstall macOS over top of itself. Once in a while it may actually fix something (very rare these days). Or you can try installing macOS to a newly created APFS volume.

Otherwise your only option would be to have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate.

Here is an Apple article for troubleshooting charing issues just in case it is a charing issue with the power on issue:

If your USB-C power adapter isn't charging your Mac laptop - Apple Support

I don't think your Mac has Magsafe, but just in case it does:

If your MagSafe cable or power adapter isn't working - Apple Support

Make sure no other external devices are attached to either Mac.

You may also want to try using a different USB-C cable.

And try using another USB port on the host Mac (the working Mac, the one with Apple Configurator or with Finder controlling the DFU options).

Maybe try booting the host Mac into Safe Mode and trying to initiate the "Revive" or "Restore" that way in case you have some third party software installed which is interfering with the normal operation of macOS.

Unfortunately there isn't much troubleshooting you can do on these newer systems. It is very frustrating since you can never be sure that the cable or the one port on the Mac necessary for DFU Mode are working correctly. I've been finding the people responsible for designing these systems obviously never have to actually support or repair them on a daily basis or we would have much better designs. It is all about form & glitz over everything else these days. It isn't just Apple either.

You may need to have Apple or an Apple Authorized Service Provider examine the Mac to see if they can do anything, or if it requires a hardware repair.

You can always provide Apple with product feedback:

Product Feedback - Apple