### 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
which->set_text(0, new_name);
	}
	if (new_name == n->get_name()) {
		if (which->get_text(0).is_empty()) {
			which->set_text(0, new_name);
		}
		return;
	}
	// Trim leading/trailing whitespace to prevent node names from containing accidental whitespace, which would make it more difficult to get the node via `get_node()`.
	new_name = new_name.strip_edges();
	if (n->is_unique_name_in_owner() && get_tree()->get_edited_scene_root()->get_node_or_null("%" + new_name) != nullptr) {
		error->set_text(TTR("Another node already uses this unique name in the scene."));
		error->popup_centered();
		which->set_text(0, n->get_name());
		return;
	}
	if (!is_scene_tree_dock) {
		n->set_name(new_name);
		which->set_metadata(0, n->get_path());
		emit_signal(SNAME("node_renamed"));
	} else {
		EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
		undo_redo->create_action(TTR("Rename Node"), UndoRedo::MERGE_DISABLE, n);
		emit_signal(SNAME("node_prerename"), n, new_name);
		undo_redo->add_do_method(this, "_rename_node", n->get_instance_id(), new_name);
		undo_redo->add_undo_method(this, "_rename_node", n->get_instance_id(), n->get_name());
		undo_redo->commit_action();
	}
}
Node *SceneTreeEditor::get_selected() {