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Authy got hacked, and 33 million user phone numbers were stolen
(appleinsider.com)
This is a most excellent place for technology news and articles.
Exporting data from a 2FA app sounds like the opposite of secure. Not to mention you don't want your 2FA codes on Authy (or any other 2FA app) to remain valid if you're not using it.
When I switched from Google Authenticator to Authy years ago, I went through each 2FA-enabled account one by one to disable 2FA and then re-enable it using Authy. It's a long process depending on how many accounts you have 2FA enabled on, but it's worth it.
Reading the OP, looks like it's time to generate new keys for all my 2FA accounts.
If you can't export / save / transfer codes then you need to regenerate all your 2fa codes every time you switch to a new device.
2FA doesn't need to be infallible, it just needs to be a second factor.