### 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
String node_name = p_node->get_name();
		if (connecting_signal) {
			node_name += " " + TTR("(Connecting From)");
		}
		item->set_text(0, node_name);
		item->set_selectable(0, marked_selectable);
		item->set_custom_color(0, get_theme_color(SNAME("accent_color"), SNAME("Editor")));
	} else if (!p_node->can_process()) {
		item->set_custom_color(0, get_theme_color(SNAME("disabled_font_color"), SNAME("Editor")));
	} else if (!marked_selectable && !marked_children_selectable) {
		Node *node = p_node;
		while (node) {
			if (marked.has(node)) {
				item->set_selectable(0, false);
				item->set_custom_color(0, get_theme_color(SNAME("error_color"), SNAME("Editor")));
				break;
			}
			node = node->get_parent();
		}
	}
	if (can_rename) { 
		String conf_warning = p_node->get_configuration_warnings_as_string();
		if (!conf_warning.is_empty()) {
			const int num_warnings = p_node->get_configuration_warnings().size();
			String warning_icon;
			if (num_warnings == 1) {
				warning_icon = SNAME("NodeWarning");
			} else if (num_warnings <= 3) {
				warning_icon = vformat("NodeWarnings%d", num_warnings);
			} else {