broadway: Break out websockets parsing and message processing

We need this to be able to correctly handle the recieve buffer
during message processing. Without the split we would be
recursing over the use of it.

gdk/broadway/gdkdisplay-broadway.h

@@ -83,6 +83,7 @@ struct _GdkBroadwayDisplay
   BroadwayOutput *output;
   guint32 saved_serial;
   BroadwayInput *input;
+  GList *input_messages;
 };
 
 struct _GdkBroadwayDisplayClass