### 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)

} else {
			memdelete(subdir);
		}
	}
	for (int i = 0; i < p_dir->get_file_count(); i++) {
		String type = p_dir->get_file_type(i);
		if (p_export_filter == EditorExportPreset::EXPORT_SELECTED_SCENES && type != "PackedScene") {
			continue;
		}
		if (type == "TextFile") {
			continue;
		}
		TreeItem *file = include_files->create_item(p_item);
		file->set_cell_mode(0, TreeItem::CELL_MODE_CHECK);
		file->set_text(0, p_dir->get_file(i));
		String path = p_dir->get_file_path(i);
		file->set_icon(0, EditorNode::get_singleton()->get_class_icon(type));
		file->set_editable(0, true);
		file->set_metadata(0, path);
		if (p_export_filter == EditorExportPreset::EXPORT_CUSTOMIZED) {
			_setup_item_for_file_mode(file, current->get_file_export_mode(path));
		} else {
			file->set_checked(0, current->has_export_file(path));
			file->propagate_check(0);
		}
		used = true;
	}
	return used;
}
void ProjectExportDialog::_propagate_file_export_mode(TreeItem *p_item, EditorExportPreset::FileExportMode p_inherited_export_mode) {