I have my duo recovery password saved in my Apple passwords but in the duo app there is no option to enter it. The support website says there should a reconnect button but there is nothing. Just a welcome page and activation stuff for making new accounts.
This looks like the UI for adding a new account in Duo Mobile. What you want to do to recover your accounts is to perform an iCloud, iTunes, or Finder restore on your phone, and then Duo Mobile should try to restore your accounts automatically and prompt you for the password.
Had you made an iCloud backup with the Keychain option enabled on your old phone?
Did you restore that to your new phone before opening Duo Mobile? When you then launched Duo Mobile did it say anything about connecting your accounts? Continuing from that prompt would ask for your recovery password to restore your third-party OTP accounts.
When I launched duo it did not say anything about connecting my accounts. The recovery password is just saved as a password in keychain under duo as “recovery password”. The recovery is password 4 or 5 years old. Could it be because my iCloud storage is full?
Ooh, yeah... if your iCloud is full then the app likely hasn't been able to create backups for however long that's been the case. You'll have to proceed to manual recovery of your accounts i.e. logging into those services with the recovery codes those services gave you at the time you configured 2FA, removing the existing 2FA app registration, and setting it up again.
