Resolve "Possible sidebar improvements based"

What does this MR do?

Cleans up the sidebar

Are there points in the code the reviewer needs to double check?

@dzaporozhets it looks like your screenshot has more padding on the left and right of the sidebar, but if you do that then the hamburger icon doesn't match the placement on the top nav, and it makes it look like icon is shifting back and forth.

What are the relevant issue numbers?

Part of #19659 (closed)

Screenshots (if relevant)