Use aegis, export the keys and then reimport them every time you switch. Trusting your second factor to a cloud is a disaster waiting to happen.
If you want to get fancy setup your own cloud server (nextcloud, Seafile, owncloud etc) and set the backup folder for aegis to the self hosted cloud for easy restore every time you switch ROMs.
Simpler approach: auto export from aegis when an update occurs, syncthing or similar to your home PC. I have it synced across several computer in different locations and aegis is good enough to make unique filenames, combine with syncthing file history and I'm good for like 2 years of backups.
Google usually goes with the lowest common denominator solution. There is a staggering amount of people who don't know what is a file, let alone that phones have any.
I've started putting mine into my Bitwarden vault as well as Google auth, mainly because I'm a bit paranoid I'll wind up locked out of something by trusting a second factor too much
I expect most usage of authy was based on the open TOTP protocol that Google etc use. The additional benefit was backing up those codes to the authy account, hence the avenue of attack on those accounts.
I agree though, Authy, especially since it was bought out, should be avoided. They deprecated their desktop app which was the only semi useful part of their suite, but I stopped using it years ago.