Certain search fields become uneditable after clearing the previous search string using the "x" button

How to reproduce:
1. Create a new project
2. Open the Package Manager (Window → Package Management → Package Manager)
3. Enter anything into the search field
4. Click the “x” button that appears on the right side of the search field
5. Without clicking anywhere else, immediately try entering text into the search field again

Expected result: The text appears in the search field
Actual result: The text does not appear in the search field

Reproducible with: 2022.1.0a5, 6000.0.61f1, 6000.2.10f1, 6000.3.0b8, 6000.4.0a3

Reproducible on: macOS 15.3.2 (24D81) (M1 Max), Windows 11 (10.0.26100) X64 (Tested by the reporter)
Not reproducible on: No other environments tested

Notes:

• The search fields lose edit mode, but not focus
• The affected search fields can be found in: Package Manager, UI Builder, UI Toolkit Debugger, Profiler, Shortcuts
• Global search, Hierarchy, Console, Project, Help tab (Menu bar) search fields work as expected
• The Package manager and UI Builder use UITK ToolbarSearchField control, while the Profiler uses IMGUI SearchField control