Search mode is exited when any resulting element is manipulated with

Steps to reproduce:

1. Create and open a new project
2. Create and open a new UI Document
3. Drag 2 Label elements and one VisualElement to the UI Builder's Hierarchy
4. Search for 'Label' in the UI Builder's Hierarchy search bar
5. Delete one of the resulting Labels
6. Observe the UI Builder's Hierarchy

Actual result: The other Label and Visual Element are displayed in the general context
Expected result: One search result "Label" is displayed in search context

Reproducible in: 6000.6.0a2
Could not test in: 6000.0.72f1, 6000.3.12f1, 6000.4.1f1, 6000.5.0b2, 6000.6.0a1 (Searching function not implemented into UI Builder)

Reproduced on: Windows 11 Pro (25H2)
Not reproduced on: No other environment tested

Note: Bug is reproducible with any element manipulation (rename, add, delete, move)