### 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
} break;
		case Animation::TYPE_ANIMATION: {
			if (!node->is_class("AnimationPlayer")) {
				EditorNode::get_singleton()->show_warning(TTR("Animation tracks can only point to AnimationPlayer nodes."));
				return;
			}
			if (node == AnimationPlayerEditor::get_singleton()->get_player()) {
				EditorNode::get_singleton()->show_warning(TTR("AnimationPlayer can't animate itself, only other players."));
				return;
			}
			EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
			undo_redo->create_action(TTR("Add Track"));
			undo_redo->add_do_method(animation.ptr(), "add_track", adding_track_type);
			undo_redo->add_do_method(animation.ptr(), "track_set_path", animation->get_track_count(), path_to);
			undo_redo->add_undo_method(animation.ptr(), "remove_track", animation->get_track_count());
			undo_redo->commit_action();
		} break;
	}
}
void AnimationTrackEditor::_add_track(int p_type) {
	if (!root) {
		EditorNode::get_singleton()->show_warning(TTR("Not possible to add a new track without a root"));
		return;
	}
	adding_track_type = p_type;
	pick_track->popup_scenetree_dialog();
	pick_track->get_filter_line_edit()->clear();
	pick_track->get_filter_line_edit()->grab_focus();
}
void AnimationTrackEditor::_new_track_property_selected(String p_name) {