Well, sex and looting, and maybe inventing new music genres.
The legend is that hip hop and sampling started after the blackout in NYC. Some electronic and music stores were looted and the recording equipment eventually ended up in the hands of musicians looking to make a new sound: https://www.rollingstone.com/music/music-features/new-york-c...
We had a (much smaller) regional (Lübeck and Ostholstein) power outage here in Northern Germany in I think 2018 or 19. No mobile internet until everything was restored ~6 hours later, and most of the time no other cell service either.
Always picture someone with a big can of diesel filling up a generator. Experience says it could be a genny running on natural gas. Had that at work before.
I think cell phone towers use surprisingly little energy, just a few kW. So even longer term operation should be possible withs bobs backyard generator running on vodka.
But I would guess the whole network equipment would draw quite a bit, especially a modern infrastructure.