Is your design idea/issue related to a use case or problem? Please describe.
After Cirq 1.0, changes to cirq-core will be backward-compatible for all minor and patch version bumps. Open questions:

• What's the scope of backward compatibility?
  • To what extent can implementation logic change?
  • Need to write down JSON serialization backward compatibility policy. JSON backwards compatibility policy and tooling. #4321
• How can we enforce backward compatibility? What CI checks do we need?
• What's the process for making an urgent patch release?