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I can confirm that with UE v22.20.0.49 on Windows XP and having enabled in configuration:

• Search - Advanced - Shift+double click highlights all words which match word under cursor
• Search - Advanced - Use persistent highlight all
• Editor Display - Cursor/Caret - Enable multi-caret editing

and executing the described steps, the persistent highlighting of the shift+double clicked word remains even after inserting a string on multiple locations in file.

I can't test same procedure at the moment with UE v23.00.0.43 as not yet available for Windows XP. I can check tomorrow on another machine with Windows 7 with UE v23.00.0.43 installed already if there is indeed a difference in persistent highlighting of double clicked word in this use case.

I can confirm this issue with UE 23.00.0.43 x64/Windows 7 SP1, Slate Theme