### 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
editor_selection->add_node(n);
		set_selected(n);
		TabContainer *tab_container = Object::cast_to<TabContainer>(NodeDock::get_singleton()->get_parent());
		NodeDock::get_singleton()->get_parent()->call("set_current_tab", tab_container->get_tab_idx_from_control(NodeDock::get_singleton()));
		NodeDock::get_singleton()->show_connections();
	} else if (p_id == BUTTON_GROUPS) {
		editor_selection->clear();
		editor_selection->add_node(n);
		set_selected(n);
		TabContainer *tab_container = Object::cast_to<TabContainer>(NodeDock::get_singleton()->get_parent());
		NodeDock::get_singleton()->get_parent()->call("set_current_tab", tab_container->get_tab_idx_from_control(NodeDock::get_singleton()));
		NodeDock::get_singleton()->show_groups();
	} else if (p_id == BUTTON_UNIQUE) {
		undo_redo->create_action(TTR("Disable Scene Unique Name"));
		undo_redo->add_do_method(n, "set_unique_name_in_owner", false);
		undo_redo->add_undo_method(n, "set_unique_name_in_owner", true);
		undo_redo->add_do_method(this, "_update_tree");
		undo_redo->add_undo_method(this, "_update_tree");
		undo_redo->commit_action();
	}
}
void SceneTreeEditor::_toggle_visible(Node *p_node) {
	if (p_node->has_method("is_visible") && p_node->has_method("set_visible")) {
		bool v = bool(p_node->call("is_visible"));
		EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
		undo_redo->add_do_method(p_node, "set_visible", !v);
		undo_redo->add_undo_method(p_node, "set_visible", v);
	}
}
void SceneTreeEditor::_add_nodes(Node *p_node, TreeItem *p_parent) {