### 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
draw_string(font, Point2(ofs, int(get_size().height - font->get_height(font_size)) / 2 + font->get_ascent(font_size)), node_name, HORIZONTAL_ALIGNMENT_LEFT, timeline->get_name_limit() - ofs, font_size, color);
			int px = (-timeline->get_value() + timeline->get_play_position()) * timeline->get_zoom_scale() + timeline->get_name_limit();
			if (px >= timeline->get_name_limit() && px < (get_size().width - timeline->get_buttons_width())) {
				Color accent = get_theme_color(SNAME("accent_color"), EditorStringName(Editor));
				draw_line(Point2(px, 0), Point2(px, get_size().height), accent, Math::round(2 * EDSCALE));
			}
		} break;
	}
}
void AnimationTrackEditGroup::gui_input(const Ref<InputEvent> &p_event) {
	ERR_FAIL_COND(p_event.is_null());
	Ref<InputEventMouseButton> mb = p_event;
	if (mb.is_valid() && mb->is_pressed() && mb->get_button_index() == MouseButton::LEFT) {
		Point2 pos = mb->get_position();
		Rect2 node_name_rect = Rect2(0, 0, timeline->get_name_limit(), get_size().height);
		if (node_name_rect.has_point(pos)) {
			EditorSelection *editor_selection = EditorNode::get_singleton()->get_editor_selection();
			editor_selection->clear();
			editor_selection->add_node(root->get_node(node));
		}
	}
}
void AnimationTrackEditGroup::set_type_and_name(const Ref<Texture2D> &p_type, const String &p_name, const NodePath &p_node) {
	icon = p_type;
	node_name = p_name;
	node = p_node;
	queue_redraw();
	update_minimum_size();
}
Size2 AnimationTrackEditGroup::get_minimum_size() const {