I'm unaware of any options to export, that would be a security issue.
To store the seed values, simply store the text provided for use if you can't use the qr code.
ISTR at least one service (AWS or Google) asking for the first 2 codes after scanning the QR code, probably to sync. So I always assumed simply re-scanning the QR code wouldn’t be enough but maybe it is this simple.
The underlying technology behind (almost?) all of these is TOTP (https://en.wikipedia.org/wiki/Time-based_One-time_Password_a...) which pretty much just depends on both systems having clocks that are reasonably close to synced. The initial value is basically a random number generator seed, and given the seed and a number of iterations (based on the time differential from a set starting point) calculating a code is fairly simple.
There would be problems on fully-isolated systems experiencing clock drift, but on any modern Internet-connected system using NTP or on any cell phone with time synced to the network it shouldn't be a factor. The most likely problem scenario is probably a corporate network using only an internal time source that drifts.
Doing a single code as validation only makes sense to catch transcription errors since in case of problems someone could end up locked out of an account.
How do you store seed values in password managers? More specifically: how do you export them from Coogle Authenticator? (I’ve not found that option). And how do you import them again?