src: handle errors correctly in webstorage

PR-URL: #54544
Backport-PR-URL: #54683
Reviewed-By: Benjamin Gruenbaum <benjamingr@gmail.com>
Reviewed-By: Anna Henningsen <anna@addaleax.net>
Reviewed-By: James M Snell <jasnell@gmail.com>
Reviewed-By: Mohammed Keyvanzadeh <mohammadkeyvanzade94@gmail.com>

Author: targos