### Godot version

v4.0.3.stable.mono.official [5222a99f5]

### System information

Windows 11

### Issue description

In the "Select a Node" windows, popped up when pressed the "Assign..." button of a `NodePath` property in the inspector.
Input any character in the "Filter Nodes" line, then clear it.

All ancestors of target type nodes become selectable.

I think it's because the correct result is supposed to be like this:
![image](https://github.com/godotengine/godot/assets/3178725/7d8ef6a2-d9f0-444e-8b18-0f251d553a1d)

but the invalid ancestors, which should be leaved in the dialog but set to unselectable, are in the wrong state.



### Steps to reproduce

- Create a new project.
- Create a new scene like this.
![image](https://github.com/godotengine/godot/assets/3178725/84acde89-a6a9-4ba7-adb4-f883531bd51a)
- Select `BoneAttachment3D` node, turn on `Use External Skeleton`
![image](https://github.com/godotengine/godot/assets/3178725/fd9fd252-253d-4a48-ba2b-764cef276738)
- Hit the "Assign..." button, open the dialog, it's good at this moment.
![image](https://github.com/godotengine/godot/assets/3178725/511d6fb8-4c83-408b-9717-0726cb7568ad)
- Input any character in the "Filter Nodes" line (like `d`).
![image](https://github.com/godotengine/godot/assets/3178725/cc60b4e4-c890-4c81-ae16-edc28fc18b57)



### Minimal reproduction project

N/A
hash = hash_djb2_one_64(p_node->get_instance_id(), hash);
	if (p_node->get_parent()) {
		hash = hash_djb2_one_64(p_node->get_parent()->get_instance_id(), hash); //so a reparent still produces a different hash
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		_compute_hash(p_node->get_child(i), hash);
	}
}
void SceneTreeEditor::_test_update_tree() {
	pending_test_update = false;
	if (!is_inside_tree()) {
		return;
	}
	if (tree_dirty) {
		return; // don't even bother
	}
	uint64_t hash = hash_djb2_one_64(0);
	if (get_scene_node()) {
		_compute_hash(get_scene_node(), hash);
	}
	//test hash
	if (hash == last_hash) {
		return; // did not change
	}
	MessageQueue::get_singleton()->push_call(this, "_update_tree");
	tree_dirty = true;
}
void SceneTreeEditor::_tree_process_mode_changed() {