I don't quite understand what you wrote :-), but I think what should happen is the least surprising thing. For me, that is that if I go through the motions of starting the extension, then I will be presented with a view of a Leo file, or an obvious offer to open one. And the Leo icon should be visible (pace vscode bugs).
I noticed that if I went back to the original vscode window and ran leointeg again, the leobridgeserver got closed and I had to restart it. I *think* I remember that the original leointeg window closed, too. If there is any way to prevent these behaviors, it would be good. It's too easy to try to open a second leointeg window (for any number of reasons; sometimes I have two Leo windows open at the same time on purpose), and either one should open without disturbing the other, or no new window should open (along with a good message about why not).