Show live online-players count on the home screen

- OnlineService.getOnlineCount(); mock random-walks a believable number,
  SignalrService reads GET /api/stats/online (server tracks hub connections)
- Home screen badge with pulsing dot, polls every 8s, localized digits

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

server/src/Hokm.Server/Game/GameManager.cs

@@ -135,9 +135,18 @@ public sealed class GameManager
     public void ChooseTrump(string userId, string suit) => RoomOf(userId)?.HumanChooseTrump(userId, suit);
     public void SendReaction(string userId, string reaction) => RoomOf(userId)?.Reaction(userId, reaction);
 
-    public void OnConnected(string userId) => RoomOf(userId)?.SetConnected(userId, true);
+    private int _online;
+    public int OnlineCount => Volatile.Read(ref _online);
+
+    public void OnConnected(string userId)
+    {
+        Interlocked.Increment(ref _online);
+        RoomOf(userId)?.SetConnected(userId, true);
+    }
+
     public void OnDisconnected(string userId)
     {
+        if (Interlocked.Decrement(ref _online) < 0) Interlocked.Exchange(ref _online, 0);
         CancelMatchmaking(userId);
         RoomOf(userId)?.SetConnected(userId, false);
     }

server/src/Hokm.Server/Program.cs

@@ -71,6 +71,7 @@ app.UseAuthentication();
 app.UseAuthorization();
 
 app.MapGet("/", () => Results.Json(new { service = "Hokm SignalR server", status = "ok" }));
+app.MapGet("/api/stats/online", (GameManager m) => Results.Json(new { online = m.OnlineCount }));
 
 // --- dev auth (mock OTP + email). Replace with the V2 Identity Service later. ---
 app.MapPost("/api/auth/otp/request", (OtpRequest req) =>