People who are still ignorant about their bitcoin will definitely end up panicking, but those who have great knowledge and knows how to deal when there is an internet connection outage, they will just stay calm and worry less. As long as bitcoin remain untouched, our bitcoin stay safe and guarded, unless conspiracy is now secretly happening.
When people already understood about Bitcoin private keys, what needed to broadcast and sign a Bitcoin transaction out of a non custodial wallet, they will feel comfortable when they don't have Internet access and have no concern about safety of their wallet and fund. If they already did right things with wallet download, installation, verification, storage, and backup, they will not feel fearful with Internet outage.
Because private keys are safe, bitcoins are safe in their non custodial wallet, with or without Internet connection. It's important when they understand this basics and can enjoy offline life for a while before Internet is back with normal traffic.
But having long internet connection outage isn't most likely to happen because the government will also not allow it as everything these days almost rely to internet. Except for those unexpected sudden internet outage that are beyond control.
It's very less likely in modern world when almost everything needs Internet to operate. Internet outage is like electricity outage, it might happen sometimes but issues will be fixed and these things will be back to serve the whole world, nations and societies.
Even it takes a longer time than our initial expectation, our bitcoin will still be safe, no worry.