Project Browser's Search by Type searching fails in AdvancedSearch if using the Type Dropdown

Steps to reproduce:

1. Create a 3D Project
2. Go to Project Preferences > Search > Search Engines and set Project to "Advanced"
3. In the Project Browser go to Assets > Button "Search by Type" > Scene
4. If only Scenes are shown remove the "Search by Type" syntax in the Search field and repeat step 3
5. If still only Scenes are shown Close and Reopen the Project and repeat step 3

Actual results: Searching by Type in the Project Browser doesn't work and all Types are always shown when searching in the "In Assets" search pill when the Search Engines Preference for Project is set to Advanced

Expected results: Searching by Type always works

Reproducible with versions: 2023.2.13f1, 2023.2.20f1, 2023.3.0b10, 6000.0.0f1

Not reproducible with versions: 2021.3.38f1, 2022.3.27f1, 2023.1.20f1, 2023.2.12f1, 2023.3.0b9

Tested on (OS): macOS Sonoma M1 (Reproducible), Windows 11 (Reproducible)

Notes:

• A workaround is to enter the Search syntax by Hand which works for that single instance