“connected via e-mail” - I don’t understand that?
The performer app supports both VST Connect SE and VST Connect PRO plugin versions, so there is no Performer PRO version as such.
If you have purchased the VST Connect PRO plugin and work on the same LAN, once Cubase is up and running just click the LAN button in the Performer login section; do not login to mySteinberg on either side. If you don’t have a PRO plugin you cannot connect within a local network.
For the WAN case (via internet): The login function connects to mySteinberg, and both sides must be logged in and thus both sides must have registered with mySteinberg. But you can also use the ID button as described before. All this is not necessary for a local connection with the PRO version.