Yesssssssss
The APC is the ticket.
Most little strips are sketchy at best.
IMHO power outages generally are not a spike issue, but rather can see a drop in voltage where the lights all dim down then finally go out.
Just having the power shut off should cause no harm.
The stove should have a lock out relay that once the power fails a reset button must be pressed to reactivate the unit.
So even if the power is off for a few seconds 2-3-5 or whatever the relay is opened and requires intervention.
The line voltage can do whatever and not hurt things.
The brown out is another story.
I have seen a couple of those, where a tree or ??? fell on the power lines and sat there smoldering until it finally caused the breakers in the line to blow.
While the tree is causing a SHORT the voltage can fall off.
Most residential feed is 7200 VOLTS prior to the transformer.
THIS STUFF burns trees and generally raises hell when it gets loose.
Bottom line, the electronics packages in most stoves today are very fragile, and when subjected to anything outside a narrow operating band GO POOOOOF
The APC is likely the best choice.