Not as sophisticated as your solution, but works with all hardware for the "backup use case": use a mechanical timer set to 10 minutes before backup starts (and power off 30 minutes after backup normally ends):

https://www.amazon.de/Mechanical-Analogue-Switching-Christma...

It's a more rigid solution that doesn't let you ssh in (unless during backup time ;-), but it saves electricity and it is implemented in 10 minutes (5 for an Amazon order and 5 to plug in and set the timer to your backup hours). It's also a more robust solution - little can go wrong (the only thing is you need to balance backup time against electricity/time savings as backup size grows).

Or just suspend to RAM on backup finish/time and use wake on RTC alarm (and set to turn on after power return on power failure if needed), no need for extra HW.