The format for emails is surprisingly complex, and while you can use a regex to catch 99% of the right values, it's very difficult to get it 100% right. Often the best thing to do is just to try and send an email to the address a validation link.
Check that its a string containing '@' with at least one character before and after the @ symbol is usually the only sensible thing to do.
This would reject valid email addresses using quoted parts like john."@".doe@valid.example.
Edit: Looking at it closely it looks like the attempt is to reject anything with an '@' in the user part, which would be an error (e.g. john."@".doe@valid.example). Except since "\S+" also includes '@' this regex will still work, but by accident. It would reject the valid email john."\ ".doe@valid.example
/^[^@\s]+@\S+$/.test("john.\"@\".doe@valid.example") == true