[broadway] Save last event time seen

gdk/broadway/gdkdisplay-broadway.h

@@ -145,6 +145,8 @@ struct _GdkBroadwayDisplay
   guint32 saved_serial;
   BroadwayInput *input;
   GList *input_messages;
+
+  guint64 last_event_time;
 };
 
 struct _GdkBroadwayDisplayClass

gdk/broadway/gdkeventsource.c

@@ -100,6 +100,8 @@ _gdk_broadway_events_got_input (GdkDisplay *display,
 
   screen = gdk_display_get_default_screen (display);
 
+  display_broadway->last_event_time = message->base.time;
+
   switch (message->base.type) {
   case 'e': /* Enter */
     display_broadway->last_x = message->pointer.root_x;