WIP: Add multiplayer Snake game

N-player (2-8) real-time Snake game alongside Connect 4.
Lobby has tabs to switch between games. Players join via
invite link with 10-second countdown. Game loop runs at
tick-based intervals with NATS pub/sub for state sync.

Keyboard input not yet working (Datastar keydown binding
issue still under investigation).

db/gen/models.go

@@ -18,6 +18,10 @@ type Game struct {
 	CreatedAt     sql.NullTime
 	UpdatedAt     sql.NullTime
 	RematchGameID sql.NullString
+	GameType      string
+	GridWidth     sql.NullInt64
+	GridHeight    sql.NullInt64
+	MaxPlayers    int64
 }
 
 type GamePlayer struct {