Manage shop items and protect active game rooms

[mpiorowski]

Summary

• Extends Hub Admin so admins can edit existing Shop item presentation/economy fields, and tightens Rooms cleanup so active games are protected while stale open tables are removed faster.

Changes

• Hub Admin now loads reward templates and marketplace items, adds a Shop Items category, and can edit Shop item name, description, chip price, sort order, and active state.
• Admin inline editing now supports cursor movement, Delete, Home, and End.
• Room games now publish in_round/open status updates so cleanup can distinguish active rounds from idle tables.
• Inactive open game rooms are hard-deleted after 1 hour, including their associated game chat through existing cascades.
• Active-room input touches room activity at most once per minute.
• Startup reconciles stale in_round rooms after restart, preserving only active durable Chess rounds.
• Includes small Door Games and pet inline UI polish.

Behavior notes

• Admin Shop editing does not add SKUs or edit item kind, slot, payload, or schedule windows.
• Hard-deleting an inactive room removes the associated game chat history/membership records through DB cascades.
• Non-durable room games reset stale in_round rows to open on restart; active Chess runtime state remains protected.

Feature flags

• None

Screenshots / Video

• Not included in this draft; attach before review.

Testing

• Automated: Added late-core/tests/game_room.rs coverage for inactive open-room hard deletion, active in_round protection, and restart reconciliation. Not run locally per repo agent policy.
• Manual: Not run.