Dropdown search icon is used next to the UI Builders Library search when the search has no dropdown functionality

How to reproduce:

1. Open any project
2. Create a UI Document Asset in the Project Browser and open it
3. Observe the search field in the Library panel and the search icon to the left of it

Actual results: Search icon intended for dropdown search is used

Expected results: Search icon without the arrow next to it should be used as clicking on the search icon does not open a dropdown menu

Reproducible with: 6000.0.30f1, 6000.1.0a6

Not reproducible with: 2021.3.46f1, 2022.3.53f1 (no search field is present)

Reproducible on: Windows 11