Add shared room game state and timer UI

[halfdimension]

Adds shared multiplayer room game state and frontend timer UI.

• Adds backend room game lifecycle: WAITING, RUNNING, ENDED
• Allows only the room host to start/end a room game
• Lets room members read the same shared game timer/state
• Adds frontend room game controls and shared countdown display
• Hides Close Room while a game is running to avoid inconsistent room/game state
• Keeps shared targets, catches, and scoring out of scope
• Keeps solo/guest gameplay unchanged