GameObject can’t be added to the serialized GameObject list in the Project Settings window when using SettingsProvider

How to reproduce:
1. Open the user’s attached “UnityBugs.zip” project
2. Open Project Settings > Test > Some Scriptable Object
3. Try to add a prefab to the “Objects” list with an object picker or drag and drop
4. Observe the result

Expected result: Prefab is added to the list
Actual result: Prefab is not added to the list

Reproducible with: 2020.2.0b3, 2021.3.25f1, 2022.2.20f1, 2023.1.0b17, 2023.2.0a16
Not reproducible with: 2020.2.0b2, 2020.3.48f1

Reproduced on: macOS 13.2.1 (Intel)

Note: not reproducible when adding prefabs to ScriptableObject in the Inspector window