fix(lobby): wire OnConfirm to POST /api/game/start, save game_id to PlayerPrefs

- OnConfirm() now calls ApiClient.PostGameStart() with 4-seat config
- On success: saves BattleSeats + GameId + WsUrl to PlayerPrefs,
  loads Battleground scene
- On failure: shows inline error label (red), re-enables Confirm button
- Added StartGameRequest/Response POCOs matching routes/game.py schema
- Added _errorLabel [SerializeField] for user-facing error feedback

unity-client/Assets/Scripts/UI/Battleground/LobbySetupModal.cs

@@ -12,7 +12,10 @@ namespace CommanderAILab.UI
     /// <summary>
     /// Modal shown at Battleground scene start.
     /// Configures 4 seats (Human vs AI, deck choice, AI style).
-    /// On Confirm writes seat config to PlayerPrefs["BattleSeats"] and starts the game.
+    /// On Confirm:
+    ///   1. POSTs seat config to POST /api/game/start
+    ///   2. Saves game_id + ws_url to PlayerPrefs
+    ///   3. Loads Battleground scene
     /// </summary>
     public class LobbySetupModal : MonoBehaviour
     {
@@ -23,6 +26,9 @@ namespace CommanderAILab.UI
         [SerializeField] private Button confirmButton;
         [SerializeField] private Button cancelButton;
 
+        [Header("Feedback")]
+        [SerializeField] private TMP_Text errorLabel;     // assign in Inspector; hidden by default
+
         [SerializeField] private ApiClient apiClient;
 
         private List<string> _deckNames = new();
@@ -31,6 +37,8 @@ namespace CommanderAILab.UI
         public void Open(string savedSeatsJson)
         {
             gameObject.SetActive(true);
+            SetError(null);
+
             confirmButton.onClick.AddListener(OnConfirm);
             cancelButton.onClick.AddListener(() => SceneManager.LoadScene("MainMenu"));
 
@@ -64,19 +72,83 @@ namespace CommanderAILab.UI
             }
         }
 
-        // ── Confirm ─────────────────────────────────────────────
+        // ── Confirm → POST /api/game/start ──────────────────────
         private void OnConfirm()
         {
+            SetError(null);
+            confirmButton.interactable = false;
+
+            // Build local seat list
             var configs = new List<SeatConfig>();
             foreach (var row in seatRows)
                 configs.Add(row?.GetConfig() ?? new SeatConfig());
 
+            // Save locally so Battleground scene can read seat metadata
             PlayerPrefs.SetString("BattleSeats", JsonConvert.SerializeObject(configs));
             PlayerPrefs.Save();
-            gameObject.SetActive(false);
+
+            // Build backend request — maps local SeatConfig → StartGameRequest
+            var apiSeats = new List<ApiSeatConfig>();
+            for (int i = 0; i < configs.Count; i++)
+            {
+                var c = configs[i];
+                apiSeats.Add(new ApiSeatConfig
+                {
+                    seat_index  = i,
+                    seat_type   = c.isHuman ? "Human" : $"AI {c.aiStyle}",
+                    deck_name   = c.deckName ?? "",
+                    player_name = c.isHuman ? "Player" : $"AI {i}",
+                });
+            }
+
+            var requestJson = JsonConvert.SerializeObject(new StartGameRequest { seats = apiSeats });
+
+            apiClient.PostGameStart(
+                requestJson,
+                onSuccess: responseJson =>
+                {
+                    try
+                    {
+                        var resp = JsonConvert.DeserializeObject<StartGameResponse>(responseJson);
+                        if (resp == null || string.IsNullOrEmpty(resp.game_id))
+                        {
+                            OnStartError("Server returned an invalid response.");
+                            return;
+                        }
+
+                        // Persist game_id and ws_url so GameWebSocketClient can connect
+                        PlayerPrefs.SetString("GameId",  resp.game_id);
+                        PlayerPrefs.SetString("WsUrl",   resp.ws_url ?? $"/ws/game/{resp.game_id}");
+                        PlayerPrefs.Save();
+
+                        gameObject.SetActive(false);
+                        SceneManager.LoadScene("Battleground");
+                    }
+                    catch (Exception ex)
+                    {
+                        OnStartError($"Parse error: {ex.Message}");
+                    }
+                },
+                onError: err => OnStartError($"Failed to start game: {err}"));
+        }
+
+        private void OnStartError(string message)
+        {
+            Debug.LogError("[LobbySetupModal] " + message);
+            SetError(message);
+            confirmButton.interactable = true;
+        }
+
+        private void SetError(string message)
+        {
+            if (errorLabel == null) return;
+            errorLabel.text    = message ?? string.Empty;
+            errorLabel.gameObject.SetActive(!string.IsNullOrEmpty(message));
         }
 
         // ── Models ─────────────────────────────────────────────
+
+        /// <summary>Local / PlayerPrefs representation of a seat.</summary>
         [Serializable]
         public class SeatConfig
         {
@@ -85,6 +157,32 @@ namespace CommanderAILab.UI
             public string aiStyle;   // Aggro / Control / Combo / Political
         }
 
+        /// <summary>Matches routes/game.py SeatConfig schema.</summary>
+        [Serializable]
+        private class ApiSeatConfig
+        {
+            public int    seat_index;
+            public string seat_type;
+            public string deck_name;
+            public string player_name;
+        }
+
+        /// <summary>Matches routes/game.py StartGameRequest schema.</summary>
+        [Serializable]
+        private class StartGameRequest
+        {
+            public List<ApiSeatConfig> seats;
+        }
+
+        /// <summary>Matches routes/game.py StartGameResponse schema.</summary>
+        [Serializable]
+        private class StartGameResponse
+        {
+            public string game_id;
+            public string status;
+            public string ws_url;
+        }
+
         [Serializable] private class DecksWrapper { public List<DeckEntry> decks; }
         [Serializable] private class DeckEntry { public string name; }
     }