backend: Sync cursor visibility after startup

When the stage is technically shown depends on when the plugin decides
to do so, so don't rely on it happening when everything is setup.

Part-of: <https://gitlab.gnome.org/GNOME/mutter/-/merge_requests/2718>

src/backends/meta-backend.c

@@ -516,7 +516,15 @@ input_mapper_device_aspect_ratio_cb (MetaInputMapper    *mapper,
 }
 
 static void
-on_stage_shown_cb (MetaBackend *backend)
+on_prepare_shutdown (MetaContext *context,
+                     MetaBackend *backend)
+{
+  g_signal_emit (backend, signals[PREPARE_SHUTDOWN], 0);
+}
+
+static void
+on_started (MetaContext *context,
+            MetaBackend *backend)
 {
   MetaBackendPrivate *priv = meta_backend_get_instance_private (backend);
   ClutterSeat *seat = priv->default_seat;
@@ -525,13 +533,6 @@ on_stage_shown_cb (MetaBackend *backend)
                                            determine_hotplug_pointer_visibility (seat));
 }
 
-static void
-on_prepare_shutdown (MetaContext *context,
-                     MetaBackend *backend)
-{
-  g_signal_emit (backend, signals[PREPARE_SHUTDOWN], 0);
-}
-
 static void
 meta_backend_real_post_init (MetaBackend *backend)
 {
@@ -542,9 +543,6 @@ meta_backend_real_post_init (MetaBackend *backend)
   priv->stage = meta_stage_new (backend);
   clutter_actor_realize (priv->stage);
   META_BACKEND_GET_CLASS (backend)->select_stage_events (backend);
-  g_signal_connect_object (priv->stage, "show",
-                           G_CALLBACK (on_stage_shown_cb), backend,
-                           G_CONNECT_SWAPPED);
 
   meta_monitor_manager_setup (priv->monitor_manager);
 
@@ -595,6 +593,8 @@ meta_backend_real_post_init (MetaBackend *backend)
 
   g_signal_connect (priv->context, "prepare-shutdown",
                     G_CALLBACK (on_prepare_shutdown), backend);
+  g_signal_connect (priv->context, "started",
+                    G_CALLBACK (on_started), backend);
 }
 
 static gboolean