Unlinking project in the Project Settings does not update the Project Settings window when clicking the “Unlink project” button having to click it a second time

Steps to reproduce:

1. Create a new Unity project using the Unviversal 3D template
2. Open the Project Settings window (Edit > Project Settings)
3. Open the "Services" tab in the Project Settings window
4. Click the "Unlink project" button
5. Observe the Project Settings window

Actual results: The project is unlinked but the Project Settings window is not updated 

Expected results: The project is unlinked and the Project Settings window is updated

Reproducible with versions: 6000.3.22f1, 6000.5.8f1, 6000.6.0b8, 6000.7.0a4

Not reproducible with versions: 6000.0.81f1

Tested on (OS): MacOS Silicon Tahoe 26.5.1

Notes:

• Sometimes may need to have the new project open for about 5-10minutes for the issue to reproduce
• Sometimes after unlinking when navigating other Project Settings tabs and then coming back to the Services tab, the window shows that the Project is linked again
• Sometimes takes a few reproduction tries to reproduce the issue