Reproduction steps:
1. Open the attached “SplineIssue” project
2. Open the “Assets/SampleScene” Scene
3. Enter Play Mode
4. Observe that the Cube is moving
5. Exit Play Mode
6. In the Editor settings (Edit > Project Settings… > Editor), set the When entering Play Mode option to “Do not reload Domain or Scene“
7. Enter Play mode
8. Observe the Cube

Expected result: The Cube is moving along the Spline
Actual result: The Cube is not moving

Reproducible with: 2.6.1 (6000.0.4f1), 2.8.1 (6000.0.55f1, 6000.2.0f1, 6000.3.0a4)
Not reproducible with: 2.6.0 (6000.0.4f1)

Reproducible on: macOS Sequoia 15.5 (M1 Max), Windows 11
Not reproducible on: No other environments tested