[3.5] Mark as finished button → status change broadcast

[underscorekadji]

Milestone: 3 – Wheel & Timing Logic
Size: S (≤ 2 hours)
Labels: frontend, socket

Description

Implement 'Mark as finished' button that changes participant status and broadcasts the change.

Acceptance Criteria

• 'Mark as finished' button for Organizer
• Status change from 'active' to 'finished'
• Status change broadcast via Socket.IO
• Button only visible to Organizer
• Real-time update to all clients

Definition of Done

• PR reviewed & merged
• GitHub Actions pipeline passes (lint → build → smoke)