Steps to reproduce:

1. Create a new Unity project using the Universal 3D template
2. Enable Hierarchy V2 (Unity > Settings > General > Use new Hierarchy window)
3. Hover the mouse to the right side of the search bar
4. Observe the mouse cursor and the search bar
5. Click the left mouse button in the right side area
6. Try typing something in the search bar
7. Observe the search bar

Actual results: There is an area on the right side of the search bar in which the cursor doesn't change to the type cursor (remains default), and when clicked in that area, editing is not initiated and pressing any keys on the keyboard do not get typed in the search bar

Expected results: The whole search bar area is clickable and can type/edit when clicked, and has the type cursor

Reproducible with versions: 6000.3.0a6

Tested on (OS): macOS Silicon Sequoia 15.6

Notes:
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Becomes very apparent when the Hierarchy V2 window is resized to be smaller, half the search bar has the area that is not functioning