### 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 (EditorNode::get_singleton()->is_exiting()) {
		return; //speed up exit
	}
	if (p_node->is_connected("script_changed", callable_mp(this, &SceneTreeEditor::_node_script_changed))) {
		p_node->disconnect("script_changed", callable_mp(this, &SceneTreeEditor::_node_script_changed));
	}
	if (p_node->is_class("Node3D") || p_node->is_class("CanvasItem") || p_node->is_class("CanvasLayer") || p_node->is_class("Window")) {
		if (p_node->is_connected("visibility_changed", callable_mp(this, &SceneTreeEditor::_node_visibility_changed))) {
			p_node->disconnect("visibility_changed", callable_mp(this, &SceneTreeEditor::_node_visibility_changed));
		}
	}
	if (p_node == selected) {
		selected = nullptr;
		emit_signal(SNAME("node_selected"));
	}
}
void SceneTreeEditor::_node_renamed(Node *p_node) {
	if (p_node != get_scene_node() && !get_scene_node()->is_ancestor_of(p_node)) {
		return;
	}
	emit_signal(SNAME("node_renamed"));
	if (!tree_dirty) {
		MessageQueue::get_singleton()->push_call(this, "_update_tree");
		tree_dirty = true;
	}
}
void SceneTreeEditor::_update_tree(bool p_scroll_to_selected) {