### 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
ClassDB::bind_method("_animation_update", &AnimationTrackEditor::_animation_update);
	ClassDB::bind_method("_track_grab_focus", &AnimationTrackEditor::_track_grab_focus);
	ClassDB::bind_method("_redraw_tracks", &AnimationTrackEditor::_redraw_tracks);
	ClassDB::bind_method("_clear_selection_for_anim", &AnimationTrackEditor::_clear_selection_for_anim);
	ClassDB::bind_method("_select_at_anim", &AnimationTrackEditor::_select_at_anim);
	ClassDB::bind_method("_clear_selection", &AnimationTrackEditor::_clear_selection);
	ClassDB::bind_method(D_METHOD("_bezier_track_set_key_handle_mode", "animation", "track_idx", "key_idx", "key_handle_mode", "key_handle_set_mode"), &AnimationTrackEditor::_bezier_track_set_key_handle_mode, DEFVAL(Animation::HANDLE_SET_MODE_NONE));
	ADD_SIGNAL(MethodInfo("timeline_changed", PropertyInfo(Variant::FLOAT, "position"), PropertyInfo(Variant::BOOL, "timeline_only")));
	ADD_SIGNAL(MethodInfo("keying_changed"));
	ADD_SIGNAL(MethodInfo("animation_len_changed", PropertyInfo(Variant::FLOAT, "len")));
	ADD_SIGNAL(MethodInfo("animation_step_changed", PropertyInfo(Variant::FLOAT, "step")));
}
void AnimationTrackEditor::_pick_track_filter_text_changed(const String &p_newtext) {