Fix Client EuiManager (#10898)

* Fix EuiManager cleanup

* cleanup

* This seems to work better

Content.IntegrationTests/Tests/Cleanup/EuiManagerTest.cs

@@ -0,0 +1,34 @@
+using System.Linq;
+using System.Threading.Tasks;
+using Content.Server.Administration.UI;
+using Content.Server.EUI;
+using NUnit.Framework;
+using Robust.Server.Player;
+using Robust.Shared.IoC;
+
+namespace Content.IntegrationTests.Tests.Cleanup;
+
+public sealed class EuiManagerTest
+{
+    [Test]
+    public async Task EuiManagerRecycleWithOpenWindowTest()
+    {
+        // Even though we are using the server EUI here, we actually want to see if the client EUIManager crashes
+        for (int i = 0; i < 2; i++)
+        {
+            await using var pairTracker = await PoolManager.GetServerClient(new PoolSettings{Dirty = true});
+            var server = pairTracker.Pair.Server;
+
+            var sPlayerManager = server.ResolveDependency<IPlayerManager>();
+
+            await server.WaitAssertion(async () =>
+            {
+                var clientSession = sPlayerManager.ServerSessions.Single();
+                var eui = IoCManager.Resolve<EuiManager>();
+                var ui = new AdminAnnounceEui();
+                eui.OpenEui(ui, clientSession);
+            });
+            await pairTracker.CleanReturnAsync();
+        }
+    }
+}