### 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
Size2 ms = add_track->get_minimum_size();
	Ref<Font> font = get_theme_font(SNAME("font"), SNAME("Label"));
	int font_size = get_theme_font_size(SNAME("font_size"), SNAME("Label"));
	ms.height = MAX(ms.height, font->get_height(font_size));
	ms.width = get_buttons_width() + add_track->get_minimum_size().width + get_editor_theme_icon(SNAME("Hsize"))->get_width() + 2;
	return ms;
}
void AnimationTimelineEdit::set_zoom(Range *p_zoom) {
	zoom = p_zoom;
	zoom->connect("value_changed", callable_mp(this, &AnimationTimelineEdit::_zoom_changed));
}
void AnimationTimelineEdit::set_track_edit(AnimationTrackEdit *p_track_edit) {
	track_edit = p_track_edit;
}
void AnimationTimelineEdit::set_play_position(float p_pos) {
	play_position_pos = p_pos;
	play_position->queue_redraw();
}
float AnimationTimelineEdit::get_play_position() const {