### 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
vtypes += ",";
				}
				vtypes += Variant::get_type_name(Variant::Type(i));
			}
			for (int i = 0; i < args.size(); i++) {
				p_list->push_back(PropertyInfo(Variant::INT, vformat("%s/%d/%s", PNAME("args"), i, PNAME("type")), PROPERTY_HINT_ENUM, vtypes));
				if (args[i].get_type() != Variant::NIL) {
					p_list->push_back(PropertyInfo(args[i].get_type(), vformat("%s/%d/%s", PNAME("args"), i, PNAME("value"))));
				}
			}
		} break;
		case Animation::TYPE_BEZIER: {
			Animation::HandleMode hm = animation->bezier_track_get_key_handle_mode(track, key);
			p_list->push_back(PropertyInfo(Variant::FLOAT, PNAME("value")));
			if (hm == Animation::HANDLE_MODE_LINEAR) {
				p_list->push_back(PropertyInfo(Variant::VECTOR2, PNAME("in_handle"), PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_READ_ONLY));
				p_list->push_back(PropertyInfo(Variant::VECTOR2, PNAME("out_handle"), PROPERTY_HINT_NONE, "", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_READ_ONLY));
			} else {
				p_list->push_back(PropertyInfo(Variant::VECTOR2, PNAME("in_handle")));
				p_list->push_back(PropertyInfo(Variant::VECTOR2, PNAME("out_handle")));
			}
			p_list->push_back(PropertyInfo(Variant::INT, PNAME("handle_mode"), PROPERTY_HINT_ENUM, "Free,Linear,Balanced,Mirrored"));
		} break;
		case Animation::TYPE_AUDIO: {
			p_list->push_back(PropertyInfo(Variant::OBJECT, PNAME("stream"), PROPERTY_HINT_RESOURCE_TYPE, "AudioStream"));
			Ref<AudioStream> audio_stream = animation->audio_track_get_key_stream(track, key);
			String hint_string = vformat("0,%.4f,0.0001,or_greater", audio_stream.is_valid() ? audio_stream->get_length() : 3600.0);
			p_list->push_back(PropertyInfo(Variant::FLOAT, PNAME("start_offset"), PROPERTY_HINT_RANGE, hint_string));
			p_list->push_back(PropertyInfo(Variant::FLOAT, PNAME("end_offset"), PROPERTY_HINT_RANGE, hint_string));
		} break;