Surprisingly mobile networks seemed to stay up in Portugal. I'm not sure to what extent and if they lasted for the whole duration of the blackout. They definitely limited consumer use though.

I love in Spain and in my zone I didn't have Internet access until after 22:00, and it was sloppy at best.

0:49 and light came back, and woke us for a moment.

So yeah, you need local first POS applications.

Most mobile base stations have a limited backup battery and some have generators on site. I'd expect telephone infrastructure to have 24-48 hours of backup in the USA and I don't know why Europe would be much different.

Population density is pretty high in many European inner cities. Most of the cell sites around here are on top of apartment buildings and I doubt they have a genset. Here in central BCN the mobile network was completely offline within an hour or two of the power going out.