### 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
bool created = false;
	bool create_normal_track = p_id.track_idx < 0;
	bool create_reset_track = p_reset_wanted && track_type_is_resettable(p_id.type);
	Animation::UpdateMode update_mode = Animation::UPDATE_DISCRETE;
	if (create_normal_track || create_reset_track) {
		if (p_id.type == Animation::TYPE_VALUE || p_id.type == Animation::TYPE_BEZIER) {
			
			NodePath np;
			animation->add_track(p_id.type);
			animation->track_set_path(animation->get_track_count() - 1, p_id.path);
			PropertyInfo h = _find_hint_for_track(animation->get_track_count() - 1, np);
			animation->remove_track(animation->get_track_count() - 1); 
			if (h.type == Variant::FLOAT ||
					h.type == Variant::VECTOR2 ||
					h.type == Variant::RECT2 ||
					h.type == Variant::VECTOR3 ||
					h.type == Variant::AABB ||
					h.type == Variant::QUATERNION ||
					h.type == Variant::COLOR ||
					h.type == Variant::PLANE ||
					h.type == Variant::TRANSFORM2D ||
					h.type == Variant::TRANSFORM3D) {
				update_mode = Animation::UPDATE_CONTINUOUS;
			}
		}
	}
	EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
	if (create_normal_track) {
		if (p_create_beziers) {
			bool valid;