### 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
ERR_FAIL_COND_V(!is_inside_tree(), nullptr);
	return get_tree()->get_edited_scene_root();
}
void SceneTreeEditor::_cell_button_pressed(Object *p_item, int p_column, int p_id, MouseButton p_button) {
	if (p_button != MouseButton::LEFT) {
		return;
	}
	if (connect_to_script_mode) {
		return; 
	}
	TreeItem *item = Object::cast_to<TreeItem>(p_item);
	ERR_FAIL_COND(!item);
	NodePath np = item->get_metadata(0);
	Node *n = get_node(np);
	ERR_FAIL_COND(!n);
	EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
	if (p_id == BUTTON_SUBSCENE) {
		if (n == get_scene_node()) {
			if (n && n->get_scene_inherited_state().is_valid()) {
				emit_signal(SNAME("open"), n->get_scene_inherited_state()->get_path());
			}
		} else {
			emit_signal(SNAME("open"), n->get_scene_file_path());
		}
	} else if (p_id == BUTTON_SCRIPT) {
		Ref<Script> script_typed = n->get_script();