### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

Ref<EditorExportPreset> current = get_current_preset();
	if (current.is_null()) {
		return;
	}
	TreeItem *item = Object::cast_to<TreeItem>(p_obj);
	String path = item->get_metadata(0);
	if (item && !path.ends_with("/")) {
		bool added = item->is_checked(0);
		if (added) {
			current->add_export_file(path);
		} else {
			current->remove_export_file(path);
		}
	}
}
void ProjectExportDialog::_tree_popup_edited(bool p_arrow_clicked) {
	Rect2 bounds = include_files->get_custom_popup_rect();
	bounds.position += get_global_canvas_transform().get_origin();
	bounds.size *= get_global_canvas_transform().get_scale();
	if (!is_embedding_subwindows()) {
		bounds.position += get_position();
	}
	file_mode_popup->popup(bounds);
}
void ProjectExportDialog::_set_file_export_mode(int p_id) {