Add host-configurable match settings persisted in settings

- GameSettings: 7 match fields (mode, hunter count, hide/seek/resolve
  durations, radar ping interval/lifetime) with authored defaults
- MatchSettingSlider (new): enum-driven panel binder, seeds from
  settings, saves on change; lifetime label shows one decimal
  (invariant culture)
- MatchManager: ApplyHostMatchSettings() on StartMatch (clamped);
  phase message now carries ping interval so clients tick correctly

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

Assets/Scripts/Helper/GameSettings.cs

@@ -18,6 +18,18 @@ public static class GameSettings
         public float mouseSensitivity = global::MouseSensitivity.Default;
         public float masterVolume = global::MasterVolume.Default;
         public string playerName = "";
+
+        // Host-side match rules (Esc-menu Match Panel). Ranges are authored on the panel sliders; the
+        // values are applied server-side in MatchManager.StartMatch (with defensive clamps there).
+        // Defaults mirror the Main scene's authored MatchManager values, so a fresh Settings.json
+        // starts matches exactly like before the panel existed.
+        public int matchMode = 0; // MatchManager.MatchMode index (0 = Classic, 1 = Conversion)
+        public int matchHunterCount = 1;
+        public float matchHideDuration = 120f;
+        public float matchSeekDuration = 300f;
+        public float matchResolveDuration = 50f;
+        public float matchRadarPingInterval = 30f;
+        public float matchRadarPingLifetime = 1f;
     }
 
     private static Data _data;
@@ -60,6 +72,55 @@ public static class GameSettings
         }
     }
 
+    /// <summary>MatchManager.MatchMode enum index the host starts matches with (0 = Classic, 1 = Conversion).</summary>
+    public static int MatchModeIndex
+    {
+        get => Store.matchMode;
+        set { if (Store.matchMode != value) { Store.matchMode = value; Save(); } }
+    }
+
+    /// <summary>How many randomly chosen players become Hunters at match start.</summary>
+    public static int MatchHunterCount
+    {
+        get => Store.matchHunterCount;
+        set { if (Store.matchHunterCount != value) { Store.matchHunterCount = value; Save(); } }
+    }
+
+    /// <summary>HIDE phase length in seconds.</summary>
+    public static float MatchHideDuration
+    {
+        get => Store.matchHideDuration;
+        set { if (!Mathf.Approximately(Store.matchHideDuration, value)) { Store.matchHideDuration = value; Save(); } }
+    }
+
+    /// <summary>SEEK phase length in seconds.</summary>
+    public static float MatchSeekDuration
+    {
+        get => Store.matchSeekDuration;
+        set { if (!Mathf.Approximately(Store.matchSeekDuration, value)) { Store.matchSeekDuration = value; Save(); } }
+    }
+
+    /// <summary>RESOLUTION (result screen) phase length in seconds.</summary>
+    public static float MatchResolveDuration
+    {
+        get => Store.matchResolveDuration;
+        set { if (!Mathf.Approximately(Store.matchResolveDuration, value)) { Store.matchResolveDuration = value; Save(); } }
+    }
+
+    /// <summary>Seconds between radar ping sweeps during Seek (0 = pings disabled).</summary>
+    public static float MatchRadarPingInterval
+    {
+        get => Store.matchRadarPingInterval;
+        set { if (!Mathf.Approximately(Store.matchRadarPingInterval, value)) { Store.matchRadarPingInterval = value; Save(); } }
+    }
+
+    /// <summary>Seconds each hider radar blip stays alive before it fades.</summary>
+    public static float MatchRadarPingLifetime
+    {
+        get => Store.matchRadarPingLifetime;
+        set { if (!Mathf.Approximately(Store.matchRadarPingLifetime, value)) { Store.matchRadarPingLifetime = value; Save(); } }
+    }
+
     private static Data Load()
     {
         string path = SavePath();