Even with CBDC or btc
We still need these electricity for sending the transaction
If the power will goes down then both will run into problem like our phone our internet & Networks all rely on the power fam
Not only these but tool like satelightes /offline wallets help it a little but they are not perfect fixe solution 
Power cut is the better energy system
not just switching like how we pay
So I will say while digital money had benefit
it is not a magic solution frend when the power goo down

Like recent SPAIN outages
You can Search that in Internet "Recent Outrage in Spain "

here the commercial stopped because their was that no electricity showing  So that the main solution should be the better energy system
not just switching to digital currency