### 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_parent) {
		p_parent = tree->get_root();
		filter_term_warning.clear();
	}
	if (!p_parent) {
		// Tree is empty, nothing to do here.
		return false;
	}
	bool keep_for_children = false;
	for (TreeItem *child = p_parent->get_first_child(); child; child = child->get_next()) {
		// Always keep if at least one of the children are kept.
		keep_for_children = _update_filter(child, p_scroll_to_selected) || keep_for_children;
	}
	// Now find other reasons to keep this Node, too.
	PackedStringArray terms = filter.to_lower().split_spaces();
	bool keep = _item_matches_all_terms(p_parent, terms);