### 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
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"));
	return Vector2(0, MAX(font->get_height(font_size), icon->get_height()) + separation);
}
void AnimationTrackEditGroup::set_timeline(AnimationTimelineEdit *p_timeline) {
	timeline = p_timeline;
	timeline->connect("zoom_changed", callable_mp(this, &AnimationTrackEditGroup::_zoom_changed));
	timeline->connect("name_limit_changed", callable_mp(this, &AnimationTrackEditGroup::_zoom_changed));
}
void AnimationTrackEditGroup::set_root(Node *p_root) {
	root = p_root;
	queue_redraw();
}
void AnimationTrackEditGroup::_zoom_changed() {
	queue_redraw();
}
AnimationTrackEditGroup::AnimationTrackEditGroup() {
	set_mouse_filter(MOUSE_FILTER_PASS);
}
void AnimationTrackEditor::add_track_edit_plugin(const Ref<AnimationTrackEditPlugin> &p_plugin) {
	if (track_edit_plugins.has(p_plugin)) {
		return;
	}
	track_edit_plugins.push_back(p_plugin);
}
void AnimationTrackEditor::remove_track_edit_plugin(const Ref<AnimationTrackEditPlugin> &p_plugin) {
	track_edit_plugins.erase(p_plugin);
}
void AnimationTrackEditor::set_animation(const Ref<Animation> &p_anim, bool p_read_only) {