Fix showing a dialog multiple times (#12625)

After the dialog is displayed, always clear it out. If we don't, we won't be able to display another!

* regressed in #12517.
* [x] Fixes #12622.

src/cascadia/TerminalApp/AppLogic.cpp

@@ -348,7 +348,11 @@ namespace winrt::TerminalApp::implementation
         }
 
         _dialog = dialog;
-
+        // GH#12622: After the dialog is displayed, always clear it out. If we
+        // don't, we won't be able to display another!
+        const auto cleanup = wil::scope_exit([this]() {
+            _dialog = nullptr;
+        });
         // IMPORTANT: This is necessary as documented in the ContentDialog MSDN docs.
         // Since we're hosting the dialog in a Xaml island, we need to connect it to the
         // xaml tree somehow.