Object Picker only shows the parent Asset and not the child assets when using Advanced Object Picker

How to reproduce:

1. Open the attached project “1221974.zip”
2. Make sure that the Object Selector is set to “Advanced” in Preferences > Search
3. Select the “testParentAndChildren” GameObject in the Hierarchy window
4. From the Inspector window select the Object Picker

Expected results: All “ParentSO” Objects are visible in both the Classic and Advanced Object Picker
Actual results: The Advanced Object Picker doesn't show the child Objects of the Asset

Reproducible with: 2021.3.4f1, 2022.1.0f1, 2022.2.0a13
Could not test with: 2019.4.39f1, 2020.3.34f1, 2022.2.0a15 (needed asset does not contain child assets)

Reproduced on: macOS (Intel) Monterey 12.3.1