Ok, I am not sure if this was the proper way to do this but it worked as intended.
{{$:/core/ui/SideBarSegments/site-title}}
{{$:/core/ui/SideBarSegments/site-subtitle}}
{{$:/core/ui/SideBarSegments/page-controls}}
{{$:/core/ui/SideBarSegments/search}}
So now upon saving I have these segments in a sidebar tab
2. Now I took every of these tiddlers above mentioned, and cloned them, so they are now overriding the originals, and then deleted their '$:/tags/SideBarSegment' tag. Now after saving. The segments on the top right are gone and the tabs have shifted up.
It looks good.