src: handle errors correctly in webstorage

PR-URL: #54544
Backport-PR-URL: #54683
Reviewed-By: Benjamin Gruenbaum <[email protected]>
Reviewed-By: Anna Henningsen <[email protected]>
Reviewed-By: James M Snell <[email protected]>
Reviewed-By: Mohammed Keyvanzadeh <[email protected]>

Author: targos