Skinned Sprites fail to render after being brought to a new scene when using DontDestroyOnLoad in the Player

How to reproduce:

1. Open the attached "IN-141149" project
2. Build the project (File > Build and Run)
3. Observe the Player

Actual result: Some of the sprites are not visible
Expected result: All of the sprites are visible

Reproducible with: 13.0.1 (6000.4.0a3), 15.0.3 (6000.6.0a5)
Not reproducible with: 13.0.0 (6000.4.0a3)

Reproducible on: macOS 26.4.1 (M1 Max)
Not reproducible on: No other environments tested

Note: Not reproducible in the Editor