### 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)

if (FileAccess::exists(wrapper_path)) {
			_code_sign(p_preset, wrapper_path);
		}
	}
	if (embedded && err == OK) {
		Ref<DirAccess> tmp_dir = DirAccess::create_for_path(p_path.get_base_dir());
		err = tmp_dir->rename(pck_path, p_path);
		if (err != OK) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("PCK Embedding"), vformat(TTR("Failed to rename temporary file \"%s\"."), pck_path));
		}
	}
	
	if (export_as_zip) {
		if (FileAccess::exists(p_path)) {
			OS::get_singleton()->move_to_trash(p_path);
		}
		Ref<FileAccess> io_fa_dst;
		zlib_filefunc_def io_dst = zipio_create_io(&io_fa_dst);
		zipFile zip = zipOpen2(p_path.utf8().get_data(), APPEND_STATUS_CREATE, nullptr, &io_dst);
		zip_folder_recursive(zip, tmp_dir_path, "", pkg_name);
		zipClose(zip, nullptr);
		if (tmp_app_dir->change_dir(tmp_dir_path) == OK) {
			tmp_app_dir->erase_contents_recursive();
			tmp_app_dir->change_dir("..");
			tmp_app_dir->remove(pkg_name);
		}
	}
	return err;
}
String EditorExportPlatformWindows::get_template_file_name(const String &p_target, const String &p_arch) const {