### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
callable_mp_static(&EditorNode::_file_access_close_error_notify_impl).bind(p_str).call_deferred();
}
void EditorNode::_file_access_close_error_notify_impl(const String &p_str) {
	add_io_error(vformat(TTR("Unable to write to file '%s', file in use, locked or lacking permissions."), p_str));
}
void EditorNode::_notify_scene_updated(Node *p_node) {
	Skeleton3D *skel_3d = Object::cast_to<Skeleton3D>(p_node);
	if (skel_3d) {
		skel_3d->reset_bone_poses();
	} else {
		BoneAttachment3D *attachment = Object::cast_to<BoneAttachment3D>(p_node);
		if (attachment) {
			attachment->notify_rebind_required();
		}
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		_notify_scene_updated(p_node->get_child(i));
	}
}
void EditorNode::reload_scene(const String &p_path) {