feat: add connection status indicator with SSE heartbeat

- Add ConnectionIndicator component showing green/red dot
- Send lastPing signal every 15 seconds via SSE
- Indicator turns red if no ping received in 20 seconds
- Gives users confidence the live connection is active

features/snakegame/handlers.go

@@ -4,6 +4,7 @@ import (
 	"fmt"
 	"net/http"
 	"strconv"
+	"time"
 
 	"github.com/alexedwards/scs/v2"
 	"github.com/go-chi/chi/v5"
@@ -123,11 +124,21 @@ func HandleSnakeEvents(snakeStore *snake.SnakeStore, nc *nats.Conn, sm *scs.Sess
 			return sse.PatchElementTempl(pages.GameContent(sg, mySlot, chatMessages(), chatCfg, gameID))
 		}
 
-		// Send initial render
+		sendPing := func() error {
+			return sse.PatchSignals([]byte(fmt.Sprintf(`{"lastPing":%d}`, time.Now().UnixMilli())))
+		}
+
+		// Send initial render and ping
+		if err := sendPing(); err != nil {
+			return
+		}
 		if err := patchAll(); err != nil {
 			return
 		}
 
+		heartbeat := time.NewTicker(15 * time.Second)
+		defer heartbeat.Stop()
+
 		// Subscribe to game updates via NATS
 		gameCh := make(chan *nats.Msg, 64)
 		gameSub, err := nc.ChanSubscribe(snake.GameSubject(gameID), gameCh)
@@ -151,6 +162,11 @@ func HandleSnakeEvents(snakeStore *snake.SnakeStore, nc *nats.Conn, sm *scs.Sess
 			case <-ctx.Done():
 				return
 
+			case <-heartbeat.C:
+				if err := sendPing(); err != nil {
+					return
+				}
+
 			case <-gameCh:
 				// Drain backed-up game updates
 				for {