AnimatorControllerPlayable does not take effect when Timeline processors are running

Unity: Mecanim Animation

2023.3.X

2023.2.X

2023.1.X

2022.3.X

2022.2.X

2021.3.X

2020.3.X

How to reproduce:
1. Download and open the attached project
2. Open the "SimpleTimelineScene" scene
3. Enter "Play" mode

Expected outcome: The characters in the scene are animated
Actual outcome: The characters in the scene are not animated

Reproducible with: 2020.3.46f1, 2021.3.21f1, 2022.2.11f1, 2023.1.0b8, 2023.2.0a6