Maybe it could be solved with Allow Multiple search panes at the same time
For example Main search pane in sidebar would be target of hotkey “Search in all files” which replaces search string by selected text as it does now. While other search panes not targeted by this hotkey would as a side-effect retain it’s search string. They can be activated conveniently by Hotkey to "Focus on last active pane".
Also concept of “cursor”/“current line” should be introduced into lists of search results and backlinks, that would keep last selected result highlighted while switching between panes. Similarly to edit mode: Improving visibility of caret(cursor) position in editor mode