### Godot version

4.0.stable

### System information

Windows 10, Forward+, GTX 1070 driver 528.49

### Issue description

When trying to edit the handle mode of a bezier cruve key from the inspector tab, the mode doesn't change. It works fine when right clicking on the key and setting the handle mode from here though. 

https://user-images.githubusercontent.com/24484962/222379540-29d71b6d-ff0c-4a21-9905-9750d0581fda.mp4



### Steps to reproduce

On an animation track using a bezier curve, select a key and try to change the handle mode from the inspector tab

### Minimal reproduction project

N/A
return root_path;
}
void AnimationTrackKeyEdit::set_use_fps(bool p_enable) {
	use_fps = p_enable;
	notify_property_list_changed();
}
void AnimationMultiTrackKeyEdit::_bind_methods() {
	ClassDB::bind_method(D_METHOD("_update_obj"), &AnimationMultiTrackKeyEdit::_update_obj);
	ClassDB::bind_method(D_METHOD("_key_ofs_changed"), &AnimationMultiTrackKeyEdit::_key_ofs_changed);
	ClassDB::bind_method(D_METHOD("_hide_script_from_inspector"), &AnimationMultiTrackKeyEdit::_hide_script_from_inspector);
	ClassDB::bind_method(D_METHOD("_hide_metadata_from_inspector"), &AnimationMultiTrackKeyEdit::_hide_metadata_from_inspector);
	ClassDB::bind_method(D_METHOD("get_root_path"), &AnimationMultiTrackKeyEdit::get_root_path);
	ClassDB::bind_method(D_METHOD("_dont_undo_redo"), &AnimationMultiTrackKeyEdit::_dont_undo_redo);
	ClassDB::bind_method(D_METHOD("_is_read_only"), &AnimationMultiTrackKeyEdit::_is_read_only);
}
void AnimationMultiTrackKeyEdit::_fix_node_path(Variant &value, NodePath &base) {
	NodePath np = value;
	if (np == NodePath()) {
		return;
	}
	Node *root = EditorNode::get_singleton()->get_tree()->get_root();
	Node *np_node = root->get_node(np);
	ERR_FAIL_NULL(np_node);
	Node *edited_node = root->get_node(base);
	ERR_FAIL_NULL(edited_node);
	value = edited_node->get_path_to(np_node);
}
void AnimationMultiTrackKeyEdit::_update_obj(const Ref<Animation> &p_anim) {