Reproduction steps:
1. Open the attached "PROJECTFILE" project
2. Open the "Assets/Scenes/SampleScene.unity" scene
3. Click on the “Assets/Scenes/test.spriteatlasv2” Sprite Atlas file
4. In the Inspector window, remove the “door” Prefab in the Objects for Packing property
5. Enter the Play mode

Expected result: “Inspector - Unsaved Changes Detected” popup window appears and after saving changes two different Sprites can be seen in the Game view (one is blue and the other is with colors)
Actual result: The changes done in the Inspector window are not saved and two blue Sprites can be seen in the Game view

Reproducible with: 2021.3.31f1
Not reproducible with: 2022.3.11f1, 2023.1.16f1, 2023.2.0b13, 2023.3.0a9
Couldn't test with: 2022.1.24f1, 2022.2.20f1, 2022.3.1f1 (Inconsistent results, different blue and colorful Sprites appear in the Play mode even though Objects for Packing has the “door” Prefab)

Reproducible on: macOS Ventura 13.6 (M1 Max)
Not reproducible on: No other environment tested