Validate room entry and expand turn alerts

[mpiorowski]

Summary

• Prevent stale or deleted room snapshot rows from opening active game backends by revalidating a room through RoomsService before entry completes.
• Broaden "your turn" desktop notifications so they can cover multiple room games and durable Chess turns, even when the user is away from the table.

Changes

• Room entry now starts an async validation task and completes only after RoomsEvent::EnterReady.
• Failed room entry refreshes the room list, clears stale active-room state, and shows an error banner.
• Deleted active rooms now prune both the visible active room and any matching active game backend.
• Turn notifications now scan room managers by room instead of only checking the currently active backend, with support added for Blackjack, Chess, Poker, and Tic-Tac-Toe.

Behavior notes

• Chess can report pending turns from persisted runtime_state after restart; other games still depend on live process-local managers.
• Notifications are suppressed while the user is viewing the same active room and are tracked independently per room.

Feature flags

• None.

Screenshots / Video

• Not included in this draft; attach before review.

Testing

• Automated: Not run. This PR description was generated from the diff context, and repo policy leaves cargo test/nextest/clippy to the human owner.
• Manual: Not run.