Aegis, available in F-droid as well, is an open source solution that allows you to easily backup and restore your TOTP "devices" (or rather, keys). You'd have

Aegis, available in F-droid as well, is an open source solution that allows you to easily backup and restore your TOTP "devices" (or rather, keys). You'd have to transfer that backup manually between your old and new phone. A more user friendly cloud solution might be Authy that others have recommended.