Bitcoin needs the internet connection to function, while goTenna only works for regional or local blackout because its devices have a max range of about 3 to 4 miles.
in terms of a global event like a nuclear war that could terminate the internet, then nothing we can do about it, forget about bitcoin, paper money, banking system, etc, prepared for stock supplies and ammo to survive.
The future of banking might happen through blockchain technology and bitcoin in mass adoption. By that time what will happen with the banking process if there happens a termination of internet connectivity for few days time.
If there is a problem with the internet connection, assume it just for a few days, then there are some solutions like
mesh network such as goTenna or
Locha mesh, and
The Blockstream Satellite Network,
to transmitting messages, data, bitcoin transactions, and services completely off-grid without having to rely on an Internet connection or even the electrical grid due to battery-powered and could also use solar panels.