### 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
time_icon = memnew(TextureRect);
	time_icon->set_v_size_flags(SIZE_SHRINK_CENTER);
	time_icon->set_tooltip_text(TTR("Animation length (seconds)"));
	len_hb->add_child(time_icon);
	length = memnew(EditorSpinSlider);
	length->set_min(0.0001);
	length->set_max(36000);
	length->set_step(0.0001);
	length->set_allow_greater(true);
	length->set_custom_minimum_size(Vector2(70 * EDSCALE, 0));
	length->set_hide_slider(true);
	length->set_tooltip_text(TTR("Animation length (seconds)"));
	length->connect("value_changed", callable_mp(this, &AnimationTimelineEdit::_anim_length_changed));
	len_hb->add_child(length);
	loop = memnew(Button);
	loop->set_flat(true);
	loop->set_tooltip_text(TTR("Animation Looping"));
	loop->connect("pressed", callable_mp(this, &AnimationTimelineEdit::_anim_loop_pressed));
	loop->set_toggle_mode(true);
	len_hb->add_child(loop);
	add_child(len_hb);
	add_track->hide();
	add_track->get_popup()->connect("index_pressed", callable_mp(this, &AnimationTimelineEdit::_track_added));
	len_hb->hide();
	panner.instantiate();
	panner->set_callbacks(callable_mp(this, &AnimationTimelineEdit::_pan_callback), callable_mp(this, &AnimationTimelineEdit::_zoom_callback));
	panner->set_pan_axis(ViewPanner::PAN_AXIS_HORIZONTAL);
	set_layout_direction(Control::LAYOUT_DIRECTION_LTR);
}
void AnimationTrackEdit::_notification(int p_what) {