That’s good that you saw that button, this was the point of my post.
Did you click on it? If you did, you have also seen the little drop down menu where you select the the LAN ip address to which you can connect. If you did connect, at the bottom edge of the window you would have also noticed the words, 'connected to '. Did you?
Regarding your wonder about the license: LAN connections work if you have an active VST Connect Pro license. Obviously, when it expires, you will revert to the SE version, with its limitations. It’s that simple. End of story. Period. Point finale. This is what is stated on the product page on the Steinberg website. If you are still wondering about whether that’s so or not, you’re focusing on the wrong elements of the story, and sabotaging your efforts to understand.