I’m reasonably certain that the giant room sized banks of batteries that they formerly kept at the CO (along with the tons of copper twisted pair) are no longer extant, which would mean that any battery backup is at the local switch cabinet.
I’ve never had VOIP, but I’m also reasonably certain that I’m only twisted pair for "the last mile"a
The abandonment of the 99.999 available PSTN is one of the tragedies of the modern era.