Reproduction steps:
1. Open the attached project 'PrefabReferenceBug'
2. Open the 'SampleScene' Scene from the 'Scenes' folder
3. Select the 'Other Prefab' Game Object in the Hierarchy
4. Drag and drop the 'Thing Prefab' Game Object from the Assets folder to the 'Other Thing' property
5. Enter the Play Mode

Expected result: The 'Other Thing' property remained set to 'Thing Prefab'
Actual result: The 'Other Thing' property switched back to 'Other Prefab'

Reproducible with: 2019.4.36f1, 2020.3.30f1, 2021.2.14f1, 2022.1.0b9, 2022.2.0a6

Note:
- If you create another prefab with 'Thing' Component, and set that new Prefab as the value of 'Other Thing' Property of the 'Other Prefab' Game Object and Enter and Exit Play Mode, and then repeat steps 2-4, the bug is not reproducible anymore