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/common/components/shared.templ

@@ -44,6 +44,21 @@ templ NicknamePrompt(returnPath string) {
 	</main>
 }
 
+// ConnectionIndicator shows a small dot indicating SSE connection status.
+// It requires a `lastPing` signal (unix ms timestamp) to be set by the server.
+templ ConnectionIndicator() {
+	<div
+		id="connection-indicator"
+		class="fixed top-2 right-2 flex items-center gap-1 text-xs text-gray-500"
+		title="Connection status"
+	>
+		<span
+			class="w-2 h-2 rounded-full transition-colors duration-300"
+			data-class="{'bg-green-500': Date.now() - $lastPing < 20000, 'bg-red-500': Date.now() - $lastPing >= 20000}"
+		></span>
+	</div>
+}
+
 templ GameJoinPrompt(loginURL string, registerURL string, gamePath string) {
 	<main class="max-w-sm mx-auto mt-8 text-center">
 		<h1 class="text-3xl font-bold">Join Game</h1>