"A recovery key has been set" but remains invisible with macOS FileVault
Yes, it is correct to assume that macOS handles the recovery key internally and securely. There's no need for you to write something down.

In case you need to do recovery because you have forgotten your login password, you can use your iCloud account to unlock FileVault. Just make sure you can remember your iCloud login details!

When you choose to use iCloud as your recovery mechanism, the settings will still show that a recovery key has been setup - so that's perfectly normal! There's no option in the settings to display the recovery key to you.