Particle System's "Texture Sheet Animation" module fails to load Sprite Atlas texture after exiting the Play Mode

Reproduction steps:
1. Open the attached “repro_IN-73151“ project
2. Open the “/Assets/Scenes/Bug.unity“ Scene
3. Make sure that in the “/Assets/Atlas.spriteatlas“, the “Include to Build“ parameter is disabled
4. Make sure that the “Edit → Project Settings… → Editor → Sprite Packer → Mode“ is set to “Sprite Atlas V1 - Always Enabled“
5. Enter the Play Mode
6. Notice that both “Image“ GameObject texture and “VFX“ GameObject texture became white
7. Exit the Play Mode
8. Observe the “VFX“ GameObject texture

Expected result: The original texture is displayed
Actual result: The texture becomes a white square

Reproducible with: 2021.3.37f1, 2022.3.24f1, 2023.2.19f1, 6000.0.0b15

Reproducible on: Windows 11 (10.0.22631) (user’s), Windows 10 (22H2)
Not reproducible on: No other environments tested

Notes:

• On step 6, the textures becoming white is an expected result because we have “Include in Build“ disabled and the Sprite Atlas reference is not provided via the SpriteAtlasManager
• In order for the correct “VFX“ GameObject texture to be restored, you’ll need to extract the archive of the project again, as the deletion of the Library folder doesn’t restore the texture