Implement IXmlTextWriterInitializer on the async writer wrapper. (#73730)

* Implement IXmlTextWriterInitializer on the async writer wrapper.

* Don't use generics per PR feedback.

* Use cast in SetOutput instead of typed field.

src/libraries/System.Private.DataContractSerialization/src/System/Xml/XmlDictionaryAsyncCheckWriter.cs

@@ -3,6 +3,7 @@
 
 using System;
 using System.Collections.Generic;
+using System.Diagnostics;
 using System.IO;
 using System.Linq;
 using System.Runtime.CompilerServices;
@@ -11,13 +12,14 @@
 
 namespace System.Xml
 {
-    internal sealed class XmlDictionaryAsyncCheckWriter : XmlDictionaryWriter
+    internal sealed class XmlDictionaryAsyncCheckWriter : XmlDictionaryWriter, IXmlTextWriterInitializer
     {
         private readonly XmlDictionaryWriter _coreWriter;
         private Task? _lastTask;
 
         public XmlDictionaryAsyncCheckWriter(XmlDictionaryWriter writer)
         {
+            Debug.Assert(writer is IXmlTextWriterInitializer);
             _coreWriter = writer;
         }
 
@@ -694,5 +696,14 @@ protected override void Dispose(bool disposing)
             CheckAsync();
             CoreWriter.Dispose();
         }
+
+        public void SetOutput(Stream stream, Encoding encoding, bool ownsStream)
+        {
+            if (CoreWriter is IXmlTextWriterInitializer initializer)
+            {
+                CheckAsync();
+                initializer.SetOutput(stream, encoding, ownsStream);
+            }
+        }
     }
 }