I would say, "Do nothing." Just don't even acknowledge them. They seem to be simply guessing, bluffing, since they can't tell you don't have a camera, and that they couldn't have captured a video using control of your computer as they claim.
Sure, it's possible for them to have control of your computer, and to have pulled files that you have saved on your computer. e.g. If you or someone else using the computer did one of the "open attachments" or visit a questionable web site, installed "we will help you fix your computer" software, etc. We don't know that anything like that is actually happening though, depending on what "proof" they might have sent you.
But even if we thought they were legit, paying them $1400 isn't going to stop them from doing anything. Or at least won't be the end of what they are going to ask you to pay. So it doesn't seem smart to even consider paying anything, regardless of whether you thought they were legit or not.
Your password is not stored here on this site. Meaning if I went into the EA117 database right now, I couldn't tell you what your password is. Whatever password you enter is put though a one-way hash, and that hash is compared against a hash stored in the database. No one "learned your password from this site."
That said, yeah, there are millions of our emails and passwords out there for sale, due to hacks and breaches that have occurred in the past. You can check your email and password against places like
https://haveibeenpwned.com/, and
https://haveibeenpwned.com/Passwords or
https://monitor.firefox.com/ to confirm what's out there about you.
But the recommended action is the same regardless of whether you find yourself out there or not. Change your password regularly. Pick strong passwords. Don't use the same password across multiple sites, except for sites where you don't care that compromise of one site will compromise all of them where you used the same password.