### 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
int AnimationTimelineEdit::get_buttons_width() const {
	Ref<Texture2D> interp_mode = get_editor_theme_icon(SNAME("TrackContinuous"));
	Ref<Texture2D> interp_type = get_editor_theme_icon(SNAME("InterpRaw"));
	Ref<Texture2D> loop_type = get_editor_theme_icon(SNAME("InterpWrapClamp"));
	Ref<Texture2D> remove_icon = get_editor_theme_icon(SNAME("Remove"));
	Ref<Texture2D> down_icon = get_theme_icon(SNAME("select_arrow"), SNAME("Tree"));
	int total_w = interp_mode->get_width() + interp_type->get_width() + loop_type->get_width() + remove_icon->get_width();
	total_w += (down_icon->get_width() + 4 * EDSCALE) * 4;
	return total_w;
}
int AnimationTimelineEdit::get_name_limit() const {
	Ref<Texture2D> hsize_icon = get_editor_theme_icon(SNAME("Hsize"));
	int limit = MAX(name_limit, add_track->get_minimum_size().width + hsize_icon->get_width());
	limit = MIN(limit, get_size().width - get_buttons_width() - 1);
	return limit;
}
void AnimationTimelineEdit::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_ENTER_TREE:
		case NOTIFICATION_THEME_CHANGED: {
			panner->setup((ViewPanner::ControlScheme)EDITOR_GET("editors/panning/animation_editors_panning_scheme").operator int(), ED_GET_SHORTCUT("canvas_item_editor/pan_view"), bool(EDITOR_GET("editors/panning/simple_panning")));
			add_track->set_icon(get_editor_theme_icon(SNAME("Add")));
			loop->set_icon(get_editor_theme_icon(SNAME("Loop")));
			time_icon->set_texture(get_editor_theme_icon(SNAME("Time")));
			add_track->get_popup()->clear();
			add_track->get_popup()->add_icon_item(get_editor_theme_icon(SNAME("KeyValue")), TTR("Property Track"));
			add_track->get_popup()->add_icon_item(get_editor_theme_icon(SNAME("KeyXPosition")), TTR("3D Position Track"));
			add_track->get_popup()->add_icon_item(get_editor_theme_icon(SNAME("KeyXRotation")), TTR("3D Rotation Track"));
			add_track->get_popup()->add_icon_item(get_editor_theme_icon(SNAME("KeyXScale")), TTR("3D Scale Track"));
			add_track->get_popup()->add_icon_item(get_editor_theme_icon(SNAME("KeyBlendShape")), TTR("Blend Shape Track"));