Steps to reproduce:

1. Create a new Unity project
2. Open the "Create new Shader Graph Asset" window (Project window > right click > Create > Shader Graph > From Template...)
3. Select any template and click the "Create" button
4. Select a newly created shader graph item in the "Project" window
5. Go to the "Inspector" window and check "Use As Template"
6. Expand the "Template" section
7. Enter the template "Name" and enter the "Category" name and save the changes
8. Open the "Create new Shader Graph Asset "window again
9. Verify that the newly created template under the new category is displayed in the "Create new Shader Graph Asset" window
10. Click "+" in the "Search" field and select the "Category" item
11. Verify that the newly created category is displayed in the list
12. Select the created shader graph asset and in the "Inspector" window update its "Category" and save the changes
13. Open the "Create new Shader Graph Asset" window again
14. Verify that the update category is displayed in the "Create new Shader Graph Asset" window
15. Check the "Category' list in the "Search" field

Actual results: Category list still displays the old category name

Expected results: New category name should be displayed

Reproducible with versions: 6000.5.0a5

Can’t test with versions: 6000.0.64f1, 6000.3.3f1, 6000.4.0b4 as search functionality is not available in these streams.

Tested on (OS):  macOS - Tahoe 26.2