### 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
TreeItem *root_item = pick_track->get_scene_tree()->get_scene_tree()->get_root();
	Vector<Node *> select_candidates;
	Node *to_select = nullptr;
	String filter = pick_track->get_filter_line_edit()->get_text();
	_pick_track_select_recursive(root_item, filter, select_candidates);
	if (!select_candidates.is_empty()) {
		for (int i = 0; i < select_candidates.size(); ++i) {
			Node *candidate = select_candidates[i];
			if (((String)candidate->get_name()).to_lower().begins_with(filter.to_lower())) {
				to_select = candidate;
				break;
			}
		}
		if (!to_select) {
			to_select = select_candidates[0];
		}
	}
	pick_track->get_scene_tree()->set_selected(to_select);
}
void AnimationTrackEditor::_pick_track_select_recursive(TreeItem *p_item, const String &p_filter, Vector<Node *> &p_select_candidates) {