Search result open in a seperate page which is default and it is not part of the tree structure.
So page tree view disappear.
When you look at the Confluence official documentation website you'l l see the same behaviour.
I don 't know it can be done but you may create a search result page in your website and use it to display result in order to display the pagetree all the time. But it might be to much effort for a little achievement.
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