Backup codes. You’re supposed to print them out and put it in a fire safe or something. They’re longer and not time based and valid until you rotate them. With those you can lose everything and still access your accounts.
My KeePass database is also synchronized locally on most of my devices, so even if my server is dead I’m not really locked out, I just have annoying merge conflicts to resolve.
Also, Yubikeys. They’re nice. If whatever blackout destroys your Yubikey, you have much worse problems to worry about than checking your email.