Q. Should I copyright my book with the US Copyright office?
Your work is protected by copyright the moment you click save (or when you send it to someone in ANY recorded form). If someone uses it without your permission, that's considered copyright infringement.
But you can't sue for damages until you have an official copyright certification from Copyright.gov. When you get one, it looks like this:
As of 2020 - the fee to file an electronic Copyright (from your PDF) costs $45 and takes approx. 3 months. Apply here.
99% of my clients don't bother with is because in all likelihood, nobody is going to steal it (or if they do, they aren't likely to make any $ from it).