feat(CS): run the siege on ONE designated server (CastleSiegeServerId)

With multiple game servers each has its own map instances, so the siege ran
independently on all of them - a guild could win uncontested on an empty server's
Valley of Loren. Now the siege (tick/spawn/battle/registration) runs only on the
server whose Id == config.CastleSiegeServerId (AdminPanel-editable). Other servers
skip the siege and just mirror the shared castle owner from config so the hunting-map
gate + castle flag rewards still work everywhere. The Guardsman on non-siege servers
tells players which server to switch to.

src/GameLogic/PlugIns/PeriodicTasks/CastleSiegeEventPlugIn.cs

@@ -83,6 +83,22 @@ public sealed class CastleSiegeEventPlugIn : IPeriodicTaskPlugIn, ISupportCustom
     public static CastleSiegeContext? TryGetContext(IGameContext gameContext)
         => Contexts.TryGetValue(gameContext, out var context) ? context : null;
 
+    /// <summary>
+    /// Returns whether the given game context is the designated Castle Siege server (the siege and registration
+    /// run only there). Non-server contexts (e.g. tests) or an uninitialized context count as the siege server.
+    /// </summary>
+    /// <param name="gameContext">The game context.</param>
+    public static bool IsCastleSiegeServer(IGameContext gameContext)
+    {
+        if (gameContext is not IGameServerContext serverContext
+            || TryGetContext(gameContext) is not { } context)
+        {
+            return true;
+        }
+
+        return serverContext.Id == context.Configuration.CastleSiegeServerId;
+    }
+
     /// <inheritdoc />
     public object CreateDefaultConfig() => new CastleSiegeConfiguration();
 
@@ -110,6 +126,20 @@ public sealed class CastleSiegeEventPlugIn : IPeriodicTaskPlugIn, ISupportCustom
             context.UpdateConfiguration(liveConfig);
         }
 
+        // With multiple game servers each has its own map instances, so the siege must run on ONE designated
+        // server (CastleSiegeServerId). Other servers skip the siege entirely — they only mirror the shared
+        // castle owner from the config so the hunting-map gate + castle flag rewards still work everywhere.
+        if (!IsCastleSiegeServer(gameContext))
+        {
+            context.SyncOwnerFromConfig();
+            if (DateTime.UtcNow.Second % 15 == 0)
+            {
+                await this.BroadcastCastleFlagAsync(gameContext, context).ConfigureAwait(false);
+            }
+
+            return;
+        }
+
         await context.TickAsync(DateTime.UtcNow).ConfigureAwait(false);
 
         // During the siege, evaluate the Crown Switches (held by standing on them) and the throne capture every tick.