In my opinion, an option to automatically create a backup whenever changes are made (similar to Aegis) would be much more useful than the existing time-based backup options.

Unlike a messaging app, an authenticator doesn't receive constant updates. Most users only add or remove an account occasionally. Creating a backup immediately after those changes ensures it's always up to date, while avoiding unnecessary scheduled backups when nothing has changed.

Time-based backups (Daily, Weekly, Monthly) could still remain as an optional feature, but change-triggered backups seem like a more practical default for an authenticator app.