Reproduction steps:
1. Open the attached project “SynchronizationLost“
2. Open the “Sample Scene” Scene
3. Select the "SyncLost" GameObject
4. Add a new string entry in the “List Of Strings“ of “Data Ref“

Expected result: new string entry is added to both "Data Ref" and "Data Ref 2"
Actual result: new string entry is added to both "Data Ref" and "Data Ref 2" only after you deselect “SyncLost“ GameObject and select it again

Reproduced with: 2022.2.0a13, 2022.2.16f1, 2023.1.0b14, 2023.2.0a13
Not reproduced with: 2021.3.24f1, 2022.2.0a12
Couldn’t test with: 2020.3.47f1 (InspectorElement.FillDefaultInspector not implemented)

Reproduced on: macOS 13.0.2 (Intel), Windows 10 (user reported)

Notes: If you comment out lines 8-14 in "SyncLostMonoEditor.cs" both lists will show the new entry directly