Improve dependency injection child providers and registries

[botoddly]

Extracts the reusable dependency-injection changes from #383 into a focused foundation PR.

• Bind child service collections to their parent provider before registration
• Dispose partially built providers when construction fails
• Make inherited registration checks available during child configuration
• Make service registries mutation-safe during iteration and support registration-time ordering
• Migrate existing consumers and update DI documentation

Testing: dotnet test GameKit.slnx --no-restore