### 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
if (p_node == get_scene_node() && p_node->get_scene_inherited_state().is_valid()) {
		item->add_button(0, get_theme_icon(SNAME("InstanceOptions"), SNAME("EditorIcons")), BUTTON_SUBSCENE, false, TTR("Open in Editor"));
		String tooltip = String(p_node->get_name()) + "\n" + TTR("Inherits:") + " " + p_node->get_scene_inherited_state()->get_path() + "\n" + TTR("Type:") + " " + p_node->get_class();
		if (!p_node->get_editor_description().is_empty()) {
			tooltip += "\n\n" + p_node->get_editor_description();
		}
		item->set_tooltip_text(0, tooltip);
	} else if (p_node != get_scene_node() && !p_node->get_scene_file_path().is_empty() && can_open_instance) {
		item->add_button(0, get_theme_icon(SNAME("InstanceOptions"), SNAME("EditorIcons")), BUTTON_SUBSCENE, false, TTR("Open in Editor"));
		String tooltip = String(p_node->get_name()) + "\n" + TTR("Instance:") + " " + p_node->get_scene_file_path() + "\n" + TTR("Type:") + " " + p_node->get_class();
		if (!p_node->get_editor_description().is_empty()) {
			tooltip += "\n\n" + p_node->get_editor_description();
		}
		item->set_tooltip_text(0, tooltip);
	} else {
		StringName type = EditorNode::get_singleton()->get_object_custom_type_name(p_node);
		if (type == StringName()) {
			type = p_node->get_class();
		}
		String tooltip = String(p_node->get_name()) + "\n" + TTR("Type:") + " " + type;
		if (!p_node->get_editor_description().is_empty()) {
			tooltip += "\n\n" + p_node->get_editor_description();
		}
		item->set_tooltip_text(0, tooltip);
	}
	if (can_open_instance && is_scene_tree_dock) { // Show buttons only when necessary (SceneTreeDock) to avoid crashes.
		if (!p_node->is_connected("script_changed", callable_mp(this, &SceneTreeEditor::_node_script_changed))) {
			p_node->connect("script_changed", callable_mp(this, &SceneTreeEditor::_node_script_changed).bind(p_node));
		}
		Ref<Script> scr = p_node->get_script();