### 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
undo_redo->create_action(TTR("Animation Change Keyframe Time"), UndoRedo::MERGE_ENDS);
	if (existing != -1) {
		undo_redo->add_do_method(animation.ptr(), "track_remove_key_at_time", track, animation->track_get_key_time(track, existing));
	}
	undo_redo->add_do_method(animation.ptr(), "track_remove_key_at_time", track, key_data_cache.time);
	undo_redo->add_do_method(animation.ptr(), "track_insert_key", track, new_time, key_data_cache.value, key_data_cache.transition);
	undo_redo->add_undo_method(animation.ptr(), "track_remove_key_at_time", track, new_time);
	undo_redo->add_undo_method(animation.ptr(), "track_insert_key", track, key_data_cache.time, key_data_cache.value, key_data_cache.transition);
	if (existing != -1) {
		undo_redo->add_undo_method(animation.ptr(), "track_insert_key", track, animation->track_get_key_time(track, existing), animation->track_get_key_value(track, existing), animation->track_get_key_transition(track, existing));
	}
	
	AnimationPlayerEditor *ape = AnimationPlayerEditor::get_singleton();
	if (ape) {
		AnimationTrackEditor *ate = ape->get_track_editor();
		if (ate) {
			undo_redo->add_do_method(ate, "_clear_selection_for_anim", animation);
			undo_redo->add_undo_method(ate, "_clear_selection_for_anim", animation);
			undo_redo->add_do_method(ate, "_select_at_anim", animation, track, new_time);
			undo_redo->add_undo_method(ate, "_select_at_anim", animation, track, key_data_cache.time);
		}
	}
	undo_redo->commit_action();
}
AnimationTrackKeyEditEditor::AnimationTrackKeyEditEditor(Ref<Animation> p_animation, int p_track, real_t p_key_ofs, bool p_use_fps) {
	if (!p_animation.is_valid()) {
		return;
	}
	animation = p_animation;
	track = p_track;