I was in Spain during the blackout nearby Valencia. My phone had 3G data connectivity from 12:30 to 18:30 despite the outage. Same for the fiber signal, powering the modem&router with batteries allowed me to a working fiber connection for 4 hours.
Some neighbors with different mobile operators told me they did not have signal. It might be some operator had backup diesel generator that lasted 4 hours.
Not only the backup generator of that base station but the backup power of all the network hardware up to it. The base station could have outlasted some other parts that run out of diesel before it did and yet it did not have connectivity.
