### 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
bool is_pinned = AnimationPlayerEditor::get_singleton()->get_player() == p_node && AnimationPlayerEditor::get_singleton()->is_pinned();
			if (is_pinned) {
				item->add_button(0, get_theme_icon(SNAME("Pin"), SNAME("EditorIcons")), BUTTON_PIN, false, TTR("AnimationPlayer is pinned.\nClick to unpin."));
			}
		}
	}
	if (editor_selection) {
		if (editor_selection->is_selected(p_node)) {
			item->select(0);
		}
	}
	if (selected == p_node) {
		if (!editor_selection) {
			item->select(0);
		}
		item->set_as_cursor(0);
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		_add_nodes(p_node->get_child(i), item);
	}
	if (valid_types.size()) {
		bool valid = false;
		for (const StringName &E : valid_types) {
			if (p_node->is_class(E) ||
					EditorNode::get_singleton()->is_object_of_custom_type(p_node, E)) {
				valid = true;
				break;
			}
		}
		if (!valid) {