### 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
p_list->push_back(PropertyInfo(Variant::INT, "args/" + itos(i) + "/type", PROPERTY_HINT_ENUM, vtypes));
					if (args[i].get_type() != Variant::NIL) {
						p_list->push_back(PropertyInfo(args[i].get_type(), "args/" + itos(i) + "/value"));
					}
				}
			} break;
			case Animation::TYPE_BEZIER: {
				p_list->push_back(PropertyInfo(Variant::FLOAT, "value"));
				p_list->push_back(PropertyInfo(Variant::VECTOR2, "in_handle"));
				p_list->push_back(PropertyInfo(Variant::VECTOR2, "out_handle"));
				p_list->push_back(PropertyInfo(Variant::INT, "handle_mode", PROPERTY_HINT_ENUM, "Free,Linear,Balanced,Mirrored"));
			} break;
			case Animation::TYPE_AUDIO: {
				p_list->push_back(PropertyInfo(Variant::OBJECT, "stream", PROPERTY_HINT_RESOURCE_TYPE, "AudioStream"));
				p_list->push_back(PropertyInfo(Variant::FLOAT, "start_offset", PROPERTY_HINT_RANGE, "0,3600,0.0001,or_greater"));
				p_list->push_back(PropertyInfo(Variant::FLOAT, "end_offset", PROPERTY_HINT_RANGE, "0,3600,0.0001,or_greater"));
			} break;
			case Animation::TYPE_ANIMATION: {
				if (key_ofs_map.size() > 1) {
					break;
				}
				String animations;
				if (root_path && root_path->has_node(animation->track_get_path(first_track))) {
					AnimationPlayer *ap = Object::cast_to<AnimationPlayer>(root_path->get_node(animation->track_get_path(first_track)));
					if (ap) {
						List<StringName> anims;
						ap->get_animation_list(&anims);
						for (List<StringName>::Element *G = anims.front(); G; G = G->next()) {
							if (!animations.is_empty()) {
								animations += ",";