Steps to reproduce:

1. Create a new Unity project using the Universal 3D template
2. Create a new Lit Shader Graph (Assets > Create > Shader Graph > URP > Lit Shader Graph)
3. Double click the created Lit Shader Graph to open the Shader Graph window
4. Open the "Create Node" menu (Right click > Create Node)
5. Observe the Search bar's Search icon

Actual results: The Search icon has a dropdown visual, but it's not a dropdown

Expected results: The Search icon should not have a dropdown visual since it's not a dropdown

Reproducible with versions: 6000.0.64f1, 6000.2.15f1, 6000.3.2f1, 6000.4.0b1, 6000.5.0a3{}{}

Tested on (OS): Windows 11, MacOS Silicon Tahoe 26.0.1