I understand the principle here, but my bitwarden is on my phone, and the standard way to do TOTP on Android seems to be Google Authenticator -- and that isn't

I understand the principle here, but my bitwarden is on my phone, and the standard way to do TOTP on Android seems to be Google Authenticator -- and that isn't even password protected once someone has the phone unlocked! I find my biggest problem with TOTP is not losing the damn things when changing phone, so I want them to be stored somewhere that get synced between devices.