### 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_type(track) == Animation::TYPE_AUDIO) {
						Ref<Texture2D> use_blend_icon = blend_icon[animation->audio_track_is_use_blend(track) ? 0 : 1];
						Vector2 use_blend_icon_pos = update_mode_rect.position + (update_mode_rect.size - use_blend_icon->get_size()) / 2;
						draw_texture(use_blend_icon, use_blend_icon_pos);
					}
					
					update_mode_rect.position.y = 0;
					update_mode_rect.size.y = get_size().height;
					ofs += update_icon->get_width() + hsep / 2;
					update_mode_rect.size.x += hsep / 2;
					if (!read_only) {
						if (animation->track_get_type(track) == Animation::TYPE_VALUE || animation->track_get_type(track) == Animation::TYPE_AUDIO) {
							draw_texture(down_icon, Vector2(ofs, int(get_size().height - down_icon->get_height()) / 2));
							update_mode_rect.size.x += down_icon->get_width();
						} else if (animation->track_get_type(track) == Animation::TYPE_BEZIER) {
							update_mode_rect.size.x += down_icon->get_width();
							update_mode_rect = Rect2();
						} else {
							update_mode_rect = Rect2();
						}
					} else {
						update_mode_rect = Rect2();
					}
					ofs += down_icon->get_width();
					draw_line(Point2(ofs + hsep * 0.5, 0), Point2(ofs + hsep * 0.5, get_size().height), linecolor, Math::round(EDSCALE));
					ofs += hsep;
				}
				{