Google Authenticator

This is the app you might have gravitated towards for your Google account—because it’s made by Google—but this is actually one of the more basic authenticator apps out there. Adding accounts is easy enough at least, and just involves scanning a QR code with your phone’s camera or typing in a numerical code. You can be up and running in seconds.
Changing phones is relatively easy too, and Google guides you through the process step-by-step so you don’t suddenly find yourself locked out of your key accounts—see here for the instructions. In terms of advanced features though, an integrated dark mode is about as good as it gets, so there’s no support for multiple devices or for cloud syncing.