Note that only a relatively small (but growing)number of universities have institutional subscriptions, so a .edu address by itself doesn't mean free storage. If.you do know that your school offers Zotero storage, add your .edu email on https://www.zotero.org/settings/account and verify/validate it.
You can add your institutional email address as a backup from your account settings https://www.zotero.org/settings/account but that will only give you free unlimited storage if your institution has a subscription.
If they do, once you've added and verified the email address, you'll automatically see the unlimited storage reflected in your storage settings.
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If they do, once you've added and verified the email address, you'll automatically see the unlimited storage reflected in your storage settings.