Profiler's Hierarchy displays CPU columns instead of GPU columns when using the search feature and restarting the Play Mode

How to reproduce:
1. Open the project “IN-109726_UnityBugReport”
2. Open the Profiler, Window → Analysis → Profiler
3. Add the GPU Usage row, Profiler Modules → GPU Usage
4. Enter Play Mode
5. Click on the GPU Usage row once
6. In the Profiler's Hierarchy search bar type “screen”
7. Stop Play Mode → Start Play Mode → Stop Play Mode
8. Double click on the GPU Usage row
9. Observe the Profiler's Hierarchy columns

Expected result: The Profiler's Hierarchy displays “Overview”, “Total”, “DrawCalls”, “GPU ms” (4) columns
Actual result: The Profiler's Hierarchy displays “Overview”, “Total”, “Self”, “Calls”, “GC Alloc”, “Time ms”, “Self ms” (7) columns

Reproducible with 2023.1.0a1, 6000.0.55f1, 6000.2.0f1 (517f89d850d1), 6000.3.0a4

Reproducible on: Windows 11
Not reproducible: No other environments tested