Systems window search query is cleared when entering Play mode with domain reload enabled

How to reproduce:

1. Open the attached “IN-153378” project
2. Open the “SampleScene” scene
3. In the Unity editor’s top menu bar, select “Window” > “Entities” > “Systems”
4. In the “Systems” window’s search bar, type “init”
5. In the Unity editor, enter Play mode
6. Observe the result in the “System” window

Actual result: The search bar is empty and the “Systems” list is unfiltered after entering Play Mode
Expected result: The search query is kept when entering Play Mode

Reproducible with: 6000.5.0a6, 6000.6.2f1, 6000.7.0b1, 7000.0.0a1
Not reproducible with: 1.2.0-pre.6 (6000.0.0b11), 1.4.8 (6000.0.84f1), 1.4.8 (6000.3.24f1), 6000.5.0a5

Reproducible on: Windows 11 Enterprise (25H2)
Not reproducible on: No other environments tested