### 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
}
				if (animation->track_get_key_value(first_track, first_key).get_type() != animation->track_get_key_value(track, key).get_type()) {
					same_key_type = false;
				}
			}
		}
	}
	if (same_track_type) {
		switch (animation->track_get_type(first_track)) {
			case Animation::TYPE_POSITION_3D: {
				p_list->push_back(PropertyInfo(Variant::VECTOR3, "position"));
			} break;
			case Animation::TYPE_ROTATION_3D: {
				p_list->push_back(PropertyInfo(Variant::QUATERNION, "rotation"));
			} break;
			case Animation::TYPE_SCALE_3D: {
				p_list->push_back(PropertyInfo(Variant::VECTOR3, "scale"));
			} break;
			case Animation::TYPE_BLEND_SHAPE: {
				p_list->push_back(PropertyInfo(Variant::FLOAT, "value"));
			} break;
			case Animation::TYPE_VALUE: {
				if (same_key_type) {
					Variant v = animation->track_get_key_value(first_track, first_key);
					if (hint.type != Variant::NIL) {
						PropertyInfo pi = hint;
						pi.name = "value";
						p_list->push_back(pi);
					} else {
						PropertyHint val_hint = PROPERTY_HINT_NONE;