I think the function you're looking for â what Google Authenticator does â is simply TOTP. A timed one-time passcode.
Lots of apps will do this, although companies like Google try to mislead people into thinking their auth tokens have to come from "the cloud".
For phones I recommend Aegis Authenticator, you can get it from either Google Play or FDroid. If you want combined password manager + TOTP in one app, then give KeePass or Bitwarden a try.
FWIW, you should be aware that its not possible to configure a phone to be as secure as a laptop, since phones don't have robust virtual machine capabilities. The list of auth apps you can use in a Linux "vault" VM differs somewhat from Android.