"Show Overrides" doesn't display Prefab overrides as read-only when they are inside managed references

Reproduction steps:
1. Open the attached “SerializeRefIssues.zip” project
2. Open the “BugSampleScene” scene (Assets/BugSampleScene/BugSampleScene)
3. Unravel the “Prefab” GameObject in the Hierarchy
4. Select the “NestedPrefab” GameObject
5. Notice that both the “Name” and the “Test” properties are overridden
6. Click the ">" next to the "NestedPrefab" GameObject in the Hierarchy to open the Prefab context view
7. Enable "Show Overrides" in the Scene view header

Expected Result: Both overridden properties (“Name” and “Test”) are read-only (grayed out)
Actual Result: Only the “Test” property is grayed out and read-only

Reproducible with: 2021.3.36f1, 2022.3.21f1, 2023.2.13f1, 2023.3.0b10

Reproducible on: Windows 11
Not reproducible on: no other environment tested