Authenticator app can also stop working when you migrate to a new phone - a friend got locked out recently after migration. Apparently you need to follow some steps [0]
[0] https://www.alphr.com/transfer-google-authenticator-codes-ne...
[0] https://www.alphr.com/transfer-google-authenticator-codes-ne...
Per my understanding, if I have Authy on my Phone, the one on my PC/laptop is the backup, and vice versa - in the sense that if one dies I can use another.
Could you elaborate on the use case.
If you have ever set one of these up with a QR code, that QR scans to something like: otpauth://totp/ACME%20Co:john.doe@email.com?secret=HXDMVJECJJWSRB3HWIZR4IFUGFTMXBOZ&issuer=ACME%20Co&algorithm=SHA1&digits=6&period=30 (From: https://github.com/google/google-authenticator/wiki/Key-Uri-...). Notice all parameters I mentioned above are present, as well as a user friendly account name.
So to directly answer your question: a backup would in some way contain all the parameters above, possibly in that otpauth:// format, but could be json or something else.
I would not consider Authy to be a trustworthy backup. I assume they are storing these secrets for you and transferring them to other computers at your request. If you can't see the secret, you can't switch to a different app. (Take this last paragraph with a grain of salt, I don't know much about authy but it sounds like trouble. I use FreeOTP and other open source OTP apps).
Then you have a physical offline backup of the TOTP secret in a QR code with error correction.
Store those sheets of paper in a folder somewhere safe.
Also consider using a yubikey for TOTP -- but do a paper backup regardless.