### 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
tree->set_filter(p_filter);
}
void SceneTreeDialog::_bind_methods() {
	ClassDB::bind_method("_cancel", &SceneTreeDialog::_cancel);
	ADD_SIGNAL(MethodInfo("selected", PropertyInfo(Variant::NODE_PATH, "path")));
}
SceneTreeDialog::SceneTreeDialog() {
	set_title(TTR("Select a Node"));
	VBoxContainer *vbc = memnew(VBoxContainer);
	add_child(vbc);
	filter = memnew(LineEdit);
	filter->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	filter->set_placeholder(TTR("Filter Nodes"));
	filter->set_clear_button_enabled(true);
	filter->add_theme_constant_override("minimum_character_width", 0);
	filter->connect("text_changed", callable_mp(this, &SceneTreeDialog::_filter_changed));
	vbc->add_child(filter);
	tree = memnew(SceneTreeEditor(false, false, true));
	tree->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	tree->get_scene_tree()->connect("item_activated", callable_mp(this, &SceneTreeDialog::_select));
	vbc->add_child(tree);
	// Disable the OK button when no node is selected.
	get_ok_button()->set_disabled(!tree->get_selected());
	tree->connect("node_selected", callable_mp(this, &SceneTreeDialog::_selected_changed));
}
SceneTreeDialog::~SceneTreeDialog() {
}