My BX750MI-GR has saved my precious data on two occasions. Earlier this year, my seven year old, well used waffle iron shorted, popping loudly and sparking quite brightly in the process, probably because of all the gunk that had accumulated inside its less cleanable interior over the years. That not only made my breaker trip, but also blew the 16 amp main fuse. The UPS kicked in immediately, making a klick and a beep, which felt amazing. That was my first time ever.
As for the second time, see this post.
It does depend on the UPS. Some just connect the output to the input and attach the battery and charger to that circuit, power cuts out and the battery kicks in, replacing the input AC signal.
Others (like the one I have) just attach the charger to the input and then power the battery protected side from the battery all the time (or maybe it’s capacitors or something, I don’t really know the specifics). This produces a clean AC signal free from interference from whatever else is on the circuit (eg ever notice the lights flicker a bit when an appliance cycles on?) as well as outside factors like lightning strikes or grid overload that just slows the frequency instead of going out entirely.
It has normal surge protection but also the isolated circuit means it isn’t even directly electrically connected so surges only make it to the charger.