Harry: I have same versions OSSN and Theme. Indeed on landing page, we have the logo on the right, and once connected, centered. I'll check topbar.php

You can just see topbar.php file in your theme. I have no idea how to make search , the toggler for sidebar and logo align on same side. So maybe you can do your experiments with the changes in the file.

Michael, on the landings page its on the left correct!
After reading the message a few times, I assumed it was about the home.

Interesting Harry.
That means: Your version of the white theme has NO LANDING page anymore where people register/login?

Well I use also the white theme v8.5, but here is the floting middle. On the left you will find the search box.
So its version based?

No idea what you're asking for?
The logo of the white theme comes already left-aligned by default - as shown on openteknik's demo page.