If this is not the right name for such a feature, apologies for confusion.
Is there a way to setup my Mikrotik in such a way that it will only enable its own Wi-Fi interfaces if my other non-Mikrotik Wi-Fi access point is down?
The goal is to only have one Wi-Fi connection available for me to use at a time. I have a Wi-Fi access point placed in the most optimal location for me, but in the event of a power loss that would bring this AP down, I would like my Mikrotik (which has a benefit of being connected to an UPS) to take over its Wi-Fi duties until my AP goes back up.

Of course you do.
Tool/Netwach ping to the device, if there is no ping turn on wifi interface, if there is ping turn off wifi interface.