You are correct that the non-filer form was technically a tax return, so your "second" tax return was rejected. You need to file your 2019 tax return by mail, and write "Amended EIP return" at the top of page 1. (You don't actually need to file a formal 1040-X amended return, just your original return with the written statement.)
Although I can't say whether you are a victim of identify theft in some other way, your story by itself does not indicate identity theft. In any case, you must file a 2020 tax return, even if you were the victim of fraud before. You can file your 2020 return by email or e-file. If you e-file, you will likely have to use zero as the AGI of your 2019 return, since you did not file your 2019 return yet.
