### 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
node = node->get_parent();
			}
			item->select(0);
			item->set_as_cursor(0);
			selected = p_node;
			tree->ensure_cursor_is_visible();
		}
	} else {
		if (!p_node) {
			selected = nullptr;
		}
		_update_tree();
		selected = p_node;
	}
	if (p_emit_selected) {
		emit_signal(SNAME("node_selected"));
	}
}
void SceneTreeEditor::_rename_node(ObjectID p_node, const String &p_name) {
	Object *o = ObjectDB::get_instance(p_node);
	ERR_FAIL_COND(!o);
	Node *n = Object::cast_to<Node>(o);
	ERR_FAIL_COND(!n);
	TreeItem *item = _find(tree->get_root(), n->get_path());
	ERR_FAIL_COND(!item);
	n->set_name(p_name);
	item->set_metadata(0, n->get_path());
	item->set_text(0, p_name);
}
void SceneTreeEditor::_renamed() {