eros 0ef0dc3d78 refactor(backend): remove remaining dead code and unused constants
Drop unused Game methods, Room.id field, and backend-only sheet ring constants that duplicated frontend definitions.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
2026-06-24 10:58:35 -07:00
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