### 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
TreeItem *which = tree->get_edited();
	ERR_FAIL_COND(!which);
	NodePath np = which->get_metadata(0);
	Node *n = get_node(np);
	ERR_FAIL_COND(!n);
	String raw_new_name = which->get_text(0);
	if (raw_new_name.strip_edges().is_empty()) {
		// If name is empty, fallback to class name.
		if (GLOBAL_GET("editor/naming/node_name_casing").operator int() != NAME_CASING_PASCAL_CASE) {
			raw_new_name = Node::adjust_name_casing(n->get_class());
		} else {
			raw_new_name = n->get_class();
		}
	}
	String new_name = raw_new_name.validate_node_name();
	if (new_name != raw_new_name) {
		error->set_text(TTR("Invalid node name, the following characters are not allowed:") + "\n" + String::get_invalid_node_name_characters());
		error->popup_centered();
		if (new_name.is_empty()) {
			which->set_text(0, n->get_name());
			return;
		}