Build a feature-flagged multi-session competition room

[coder13]

Part of #199.

Goal

Prove the new Room/RaceSession model through a small user-visible competition-room flow without changing the simple normal-room experience.

Vertical slice

• Create or seed one competition room associated with a competition.
• Give it at least two event RaceSessions.
• Allow an eligible user to enter the room, choose an event session, and race.
• Keep attempts, waiting state, and results independent between sessions.
• Allow switching sessions without leaving the room.
• Preserve completed results when a session ends or another session becomes active.
• Hide the feature behind a disabled-by-default configuration flag.

UX requirements

• The ordinary home-page Create room action and copy-link flow remain unchanged.
• Normal rooms do not show competition/session-selection UI.
• Competition participants enter one room, then choose an event.
• The active session and event must always be obvious.
• Mobile layouts must not become a dashboard or require navigating a complex competition schedule.
• Unsupported or unavailable sessions show a clear, recoverable state.

Acceptance criteria

• One competition room can contain and display at least two event sessions.
• Two users can race in one session while another session retains separate state.
• Switching sessions cannot submit a solve to the wrong attempt.
• Refresh and reconnect restore the selected room/session safely.
• Permissions prevent unauthorized session creation or control.
• Ended-session results remain available to authorized users.
• Normal-room Cypress coverage proves no added step or visible complexity.
• A competition-room Cypress flow covers join → select event → solve → switch event → solve.
• The feature can be disabled without affecting normal rooms.

Deferred

• Automatic creation three days before every WCA competition.
• Complete competition discovery and registration syncing.
• Friends, invitations, notifications, rankings, and Discord integration.