What happens when my iCloud account gets breached?

This was a scam. Here is some information on how to "Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams:" https://support.apple.com/en-us/HT204759 This read also provides information on how to "report phishing attempts and other suspicious messages to Apple."

And, if you are worried that you Apple ID has been compromised, see: https://support.apple.com/en-us/HT204145If your iCloud account has been compromised, then so has your Apple ID.

Somebody used automated tools to target you for spam telephone calls, and lied to you.

You did what you were supposed to do: get frightened.

What did the folks at Apple Support tell you?

Or did you happen to call back the folks that called you, or called some number you found for “Apple Support”?

Because that would be bad. Particularly if you gave them your password. That would be very bad.

If you gave anybody your Apple ID password, change that right now! now! now! now!

If you did not give out your Apple ID password, you’re fine. Only change your password if you want.

To be blunt, all telephone calls are suspect. All.

All email messages are suspect. All.

Text messages, too.

Even emails apparently from your friends and acquaintances are suspect.

A good friend still mails me on occasion, though he died a few years ago. (The spammers don’t seem to know that.)

Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support