Locked out

It is a scam, don't do it.

See this for understanding phishing attempts and legitimate mails from Apple. Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support and this, Identify legitimate emails from the App Store or iTunes Store - Apple Support

It is NOT legit. The email was a scam. Any information you gave them is now compromised, so be prepared for your identity to be stolen. Take whatever steps are necessary to protect yourself. For example:

• If you entered your Apple ID and password, change the password IMMEDIATELY
• Add 2 factor authentication to your Apple ID if it isn’t there already
• If you entered a credit or debit card call your bank and inform them so they can cancel and reissue it
• Put a freeze on your account at the 3 major credit bureaus immediately if you don’t have this already:https://www.consumer.ftc.gov/blog/2018/09/free-credit-freezes-are-here
• Check to see if your Apple ID has been compromised on the dark web: https://haveibeenpwned.com
• That same site can also check to see if your password has been compromised
• If you shared your Apple ID password with other sites change it on those sites also

And you were right to be suspicious. Apple does not use your SSN and doesn’t ask for it. The one exception is if you apply for an Apple Card, but that goes to Goldman-Sachs, not Apple, and is used to do a credit check. It is not saved.