Add play again button for rematch after game ends

When a game finishes (win or draw), players see a "Play again" button.
Clicking it creates a new game and the opponent sees a "Join Rematch"
link to join the same game.

game/types.go

@@ -21,13 +21,14 @@ const (
 )
 
 type Game struct {
-	ID           string
-	Board        [6][7]int  // 6 rows, 7 columns; 0=empty, 1=red, 2=yellow
-	Players      [2]*Player // Index 0 = creator (Red), Index 1 = joiner (Yellow)
-	CurrentTurn  int        // 1 or 2 (matches player color)
-	Status       GameStatus
-	Winner       *Player
-	WinningCells [][2]int // Coordinates of winning 4 cells for highlighting
+	ID            string
+	Board         [6][7]int  // 6 rows, 7 columns; 0=empty, 1=red, 2=yellow
+	Players       [2]*Player // Index 0 = creator (Red), Index 1 = joiner (Yellow)
+	CurrentTurn   int        // 1 or 2 (matches player color)
+	Status        GameStatus
+	Winner        *Player
+	WinningCells  [][2]int // Coordinates of winning 4 cells for highlighting
+	RematchGameID *string  // ID of the rematch game, if one was created
 }
 
 func NewGame(id string) *Game {
@@ -39,6 +40,10 @@ func NewGame(id string) *Game {
 	}
 }
 
+func (g *Game) IsFinished() bool {
+	return g.Status == StatusWon || g.Status == StatusDraw
+}
+
 func (g *Game) BoardToJSON() string {
 	data, _ := json.Marshal(g.Board)
 	return string(data)