### 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
connect_to_script_mode = p_enable;
	update_tree();
}
void SceneTreeEditor::set_connecting_signal(bool p_enable) {
	connecting_signal = p_enable;
	update_tree();
}
void SceneTreeEditor::_bind_methods() {
	ClassDB::bind_method(D_METHOD("_update_tree"), &SceneTreeEditor::_update_tree, DEFVAL(false)); // Still used by UndoRedo.
	ClassDB::bind_method("_rename_node", &SceneTreeEditor::_rename_node);
	ClassDB::bind_method("_test_update_tree", &SceneTreeEditor::_test_update_tree);
	ClassDB::bind_method(D_METHOD("update_tree"), &SceneTreeEditor::update_tree);
	ADD_SIGNAL(MethodInfo("node_selected"));
	ADD_SIGNAL(MethodInfo("node_renamed"));
	ADD_SIGNAL(MethodInfo("node_prerename"));
	ADD_SIGNAL(MethodInfo("node_changed"));
	ADD_SIGNAL(MethodInfo("nodes_dragged"));
	ADD_SIGNAL(MethodInfo("nodes_rearranged", PropertyInfo(Variant::ARRAY, "paths"), PropertyInfo(Variant::NODE_PATH, "to_path"), PropertyInfo(Variant::INT, "type")));
	ADD_SIGNAL(MethodInfo("files_dropped", PropertyInfo(Variant::PACKED_STRING_ARRAY, "files"), PropertyInfo(Variant::NODE_PATH, "to_path"), PropertyInfo(Variant::INT, "type")));
	ADD_SIGNAL(MethodInfo("script_dropped", PropertyInfo(Variant::STRING, "file"), PropertyInfo(Variant::NODE_PATH, "to_path")));
	ADD_SIGNAL(MethodInfo("rmb_pressed", PropertyInfo(Variant::VECTOR2, "position")));
	ADD_SIGNAL(MethodInfo("open"));
	ADD_SIGNAL(MethodInfo("open_script"));
}
SceneTreeEditor::SceneTreeEditor(bool p_label, bool p_can_rename, bool p_can_open_instance) {