### 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<InputEventKey> k = p_ie;
	if (k.is_valid()) {
		switch (k->get_keycode()) {
			case Key::UP:
			case Key::DOWN:
			case Key::PAGEUP:
			case Key::PAGEDOWN: {
				pick_track->get_scene_tree()->get_scene_tree()->gui_input(k);
				pick_track->get_filter_line_edit()->accept_event();
			} break;
			default:
				break;
		}
	}
}
AnimationTrackEditor::AnimationTrackEditor() {