”Advanced” Search Engine is opened when “Classic” Search Engine is selected when using Visual Effects Graph

How to reproduce:
1. Open the user’s attached “ObjectSelectorTest.zip” project
2. Open “VFX.vfx” Visual Effects Graph
3. Press the select button of “Main Texture”
4. Observe the Search window

Expected result: Search Engine is classic
Actual result: Search Engine is advanced

Reproducible with: 13.1.1 (2022.1.0a16), 14.0.6 (2022.2.5f1), 15.0.4 (2023.1.0b2)
Not reproducible with: 10.10.1 (2020.3.44f1), 12.1.10 (2021.3.18f1), 13.1.0 (2022.1.0a15)

Reproduced on: macOS 12.4 (Intel)

Note: Search Engine is set in Preferences > Search > Search Engines > Object Selector