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.

db/persister.go

@@ -43,13 +43,19 @@ func (p *GamePersister) SaveGame(g *game.Game) error {
 		winningCells = sql.NullString{String: wc, Valid: true}
 	}
 
+	rematchGameID := sql.NullString{}
+	if g.RematchGameID != nil {
+		rematchGameID = sql.NullString{String: *g.RematchGameID, Valid: true}
+	}
+
 	return p.queries.UpdateGame(ctx, gen.UpdateGameParams{
-		Board:        g.BoardToJSON(),
-		CurrentTurn:  int64(g.CurrentTurn),
-		Status:       int64(g.Status),
-		WinnerUserID: winnerUserID,
-		WinningCells: winningCells,
-		ID:           g.ID,
+		Board:         g.BoardToJSON(),
+		CurrentTurn:   int64(g.CurrentTurn),
+		Status:        int64(g.Status),
+		WinnerUserID:  winnerUserID,
+		WinningCells:  winningCells,
+		RematchGameID: rematchGameID,
+		ID:            g.ID,
 	})
 }
 
@@ -74,6 +80,10 @@ func (p *GamePersister) LoadGame(id string) (*game.Game, error) {
 		g.WinningCellsFromJSON(row.WinningCells.String)
 	}
 
+	if row.RematchGameID.Valid {
+		g.RematchGameID = &row.RematchGameID.String
+	}
+
 	return g, nil
 }