[Fabric] Fix hang on shutdown when JS instance failed to start (#12867)

* Fix hang on shutdown when JS instance failed to start

* Change files

* dont wrap the ManualResetEvent in another shared_ptr

* use unique_ptr since there is only one ref

* fix

change/react-native-windows-ded8504d-7e64-46ef-9c94-474b8b0b7c61.json

@@ -0,0 +1,7 @@
+{
+  "type": "prerelease",
+  "comment": "[Fabric] Fix hang on shutdown when JS instance failed to start",
+  "packageName": "react-native-windows",
+  "email": "30809111+acoates-ms@users.noreply.github.com",
+  "dependentChangeType": "patch"
+}

vnext/Microsoft.ReactNative/Fabric/Composition/CompositionRootView.cpp

@@ -395,6 +395,13 @@ void CompositionRootView::UpdateRootViewInternal() noexcept {
   }
 }
 
+struct AutoMRE {
+  ~AutoMRE() {
+    mre.Set();
+  }
+  Mso::ManualResetEvent mre;
+};
+
 void CompositionRootView::UninitRootView() noexcept {
   if (!m_isInitialized) {
     return;
@@ -411,8 +418,10 @@ void CompositionRootView::UninitRootView() noexcept {
     // This is needed to ensure that the unmount JS logic is completed before the the instance is shutdown during
     // instance destruction. Aligns with similar code in ReactInstanceWin::DetachRootView for paper Future: Instead this
     // method should return a Promise, which should be resolved when the JS logic is complete.
+    // The task will auto set the event on destruction to ensure that the event is set if the JS Queue has already been
+    // shutdown
     Mso::ManualResetEvent mre;
-    m_context.JSDispatcher().Post([&]() { mre.Set(); });
+    m_context.JSDispatcher().Post([autoMRE = std::make_unique<AutoMRE>(AutoMRE{mre})]() {});
     mre.Wait();
 
     // Paper version gives the JS thread time to finish executing - Is this needed?