But the comments here indicate that there should - **probably** - be continuing broadband down the phone lines *in most cases* for a good few hours at least. That is helpful to know.
All this referring to the xDSLx scenario.
It doesn't refer to your router unless, like you, the user has a UPS. No broadband of any kind other than mobile to mobile phone if the router (or even stand-alone modem) has no on-site power backup and the power to the premises fails.
The exchange power down the line won't drive a modem or modem/router. Even if the splitter passes it through, which I don't know. (Splitters do pass both phone and broadband signals to the modem, just preventing broadband frequencies to and from the phone cable).
Also of course
if you are using a DECT phone system the base station would be dead in a power cut without backup power. You need an old type direct plug-in one.
Connections: OnePlus 8 Pro on Three 4+ (LTE)/5G and at home Three Mobile, with (Three)ZTE MF286D router giving about 113/20Mbps.
The best of all possible countries.