I get that scam email, too. It’s hilarious.
No. They haven’t remote accessed your camera, or the rest. That didn’t happen.
They’ll sometimes even send along an old password from some breach of some web service.
(Why password re-use is a Bad Idea, too.)
In addition to the above reply, here’s some more on what’s become commonplace:
Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support
Also enable two-factor authentication, as that makes wresting control of your Apple ID more difficult.
Two-factor authentication for Apple ID - Apple Support