The active game. Initial visibility values are read from this record.
The GM can independently reveal the question text, answer options, and
associated media to players. Each toggle is persisted to the games table
and broadcast via the VISIBILITY transport event so all connected players
update immediately.
Optimistic updates are applied locally before the DB write completes.
If the write fails, the previous state is restored and error is set.
Manages question-visibility state for the GM view.