### 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
animation = p_animation;
	read_only = p_read_only;
	track = p_track;
	queue_redraw();
	ERR_FAIL_INDEX(track, animation->get_track_count());
	node_path = animation->track_get_path(p_track);
	type_icon = _get_key_type_icon();
	selected_icon = get_editor_theme_icon(SNAME("KeySelected"));
}
NodePath AnimationTrackEdit::get_path() const {
	return node_path;
}
Size2 AnimationTrackEdit::get_minimum_size() const {
	Ref<Texture2D> texture = get_editor_theme_icon(SNAME("Object"));
	Ref<Font> font = get_theme_font(SNAME("font"), SNAME("Label"));
	int font_size = get_theme_font_size(SNAME("font_size"), SNAME("Label"));
	int separation = get_theme_constant(SNAME("v_separation"), SNAME("ItemList"));
	int max_h = MAX(texture->get_height(), font->get_height(font_size));
	max_h = MAX(max_h, get_key_height());
	return Vector2(1, max_h + separation);
}
void AnimationTrackEdit::set_timeline(AnimationTimelineEdit *p_timeline) {
	timeline = p_timeline;
	timeline->set_track_edit(this);
	timeline->connect("zoom_changed", callable_mp(this, &AnimationTrackEdit::_zoom_changed));
	timeline->connect("name_limit_changed", callable_mp(this, &AnimationTrackEdit::_zoom_changed));
}
void AnimationTrackEdit::set_editor(AnimationTrackEditor *p_editor) {