### Godot version

4.0.dev(dc3175e4cdb4e54e1c6200b6c4d07646eea95284)

### System information

Any

### Issue description

EditorPlugins that depend on the resources that Node has will not be visible when SubInspector is focused.

https://user-images.githubusercontent.com/61938263/210553656-86669f57-e41f-427e-a650-30630c27d850.mp4

This is caused by two problems:

The first is caused by implicit editor deletion in Node3D. This is fixed by #70907.

The other is due to a change in inspector update timing, which is regression by #68498. Revert PR #70909 will fix this issue, but if not, we will need to update SubInspectorEditor in the correct way.

### Steps to reproduce

Select Path3D or CollisionPolygon3D and open a SubInspector such as Script.

### Minimal reproduction project

[plugintest.zip](https://github.com/godotengine/godot/files/10343962/plugintest.zip)

emit_signal(SNAME("object_id_selected"), p_id);
}
void EditorInspector::_resource_selected(const String &p_path, Ref<Resource> p_resource) {
	emit_signal(SNAME("resource_selected"), p_resource, p_path);
}
void EditorInspector::_node_removed(Node *p_node) {
	if (p_node == object) {
		edit(nullptr);
	}
}
void EditorInspector::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_READY: {
			EditorFeatureProfileManager::get_singleton()->connect("current_feature_profile_changed", callable_mp(this, &EditorInspector::_feature_profile_changed));
			set_process(is_visible_in_tree());
			_update_inspector_bg();
		} break;
		case NOTIFICATION_ENTER_TREE: {
			if (!sub_inspector) {
				get_tree()->connect("node_removed", callable_mp(this, &EditorInspector::_node_removed));
			}
		} break;
		case NOTIFICATION_PREDELETE: {
			edit(nullptr); 
		} break;