Meanwhile, your recommendation (Aegis) let us copy encrypted backup file as we like.
ente Authenticator (a secondary product of ente[1]) also allows you to export your codes:
--snip--
It looks good. But it's weird the github has almost 1K stars, while it has only 1K+ download on google play[1]. So i'd continue to recommend Aegis, unless they use Apple device.
[1]
https://play.google.com/store/apps/details?id=io.ente.auth