Entering playmode with disabled compositor breaks all its layers

Versions affected: 2021.3.9f1, 2023.1.0a5 (and most probably any other version that has Compositor)

Steps to reproduce:

1) Open attached project

2) Disable compositor, switch to Display 1 in game view

3) Enter and leave playmode

4) Observe how Compositor loses connection to all its existing assets

5) If you reenable compositor it will recreate its assets and there's no way to restore layer data (only base layers that come from SG)