This is by design. The scene with the red skybox is using the skybox as the environment lighting source. When using this setting, a cubemap and light probe will be created when baking the scene, which store the environment contribution from the skybox. Since the scene with the red skybox hasn't been baked, these files are not present.
To fix the issue with the missing environment lighting, simply open the scene with the red skybox and bake it (Windows > Rendering > Lighting > Generate Lighting), and the environment lighting from the scene should appear.