Preset deletion in "Select Preset" window doesn't work

Steps to reproduce:

1. Create a project
2. Add 2D/3D game object
3. Go to "Inspector" tab
4. Select any component
5. Click on preset icon
6. Verify, that "Select Preset" window opens
7. Find "Create New XXXXX Preset ..." line
8. Create few presets
9. Observe that newly created presets are displayed in Project->Assets section
10. Open the same "Select Preset" window
11. Select a preset and from the meatball menu select "Delete"

Expected result: Selected and deleted preset should be deleted

Actual result:  Preset isn't deleted. Video added in the attachments section.

Reproducible with: 2023.1.0.a17, 2023.1.0b1
Not reproducible with:

• 2022.2.3f1 (this stream has old UI)
• 2021.3.17f1 (this one has more older UI)