Use a task chain and fix potential misordering of events

osu.Game/Utils/TaskChain.cs

@@ -0,0 +1,30 @@
+// Copyright (c) ppy Pty Ltd <contact@ppy.sh>. Licensed under the MIT Licence.
+// See the LICENCE file in the repository root for full licence text.
+
+#nullable enable
+
+using System;
+using System.Threading.Tasks;
+
+namespace osu.Game.Utils
+{
+    /// <summary>
+    /// A chain of <see cref="Task"/>s that run sequentially.
+    /// </summary>
+    public class TaskChain
+    {
+        private readonly object currentTaskLock = new object();
+        private Task? currentTask;
+
+        public Task Add(Func<Task> taskFunc)
+        {
+            lock (currentTaskLock)
+            {
+                currentTask = currentTask == null
+                    ? taskFunc()
+                    : currentTask.ContinueWith(_ => taskFunc()).Unwrap();
+                return currentTask;
+            }
+        }
+    }
+}