A copywriter is, to quote the Oxford English Dictionary, ‘someone who writes the text of advertisements or publicity material’.
Basically, a copywriter writes copy. I know… you’d never have guessed, right? And as with anyone who creates, a copywriter owns the copyright to their work.
Copyright is ‘the sole right to publish a work’, or in its verb form, ‘to secure copyright for’ something. Leaving aside the fact that you automatically own the copyright to anything you write, and there’s rarely any need to publicly claim your copyright (it generally goes without saying, kind of like not having to lay claim to your own coat while you’re actually wearing it), ‘copyrighted’ is the past tense of the verb form. As in, ‘this work is copyrighted’. Or in its noun form, ‘I own the copyright to this work’. It is not ‘copywritten’. You do not own the ‘copywrite’.
Neither ‘copywritten’ nor ‘copywrite’ are actually words. You own your writing. Not your ‘write’, copied or otherwise. Homophones (such as ‘copyright’ and ‘copywrite’) can be tricky, but even more so when they’re both used within the same field. But of course, this is the field of writing. And writers, of all people, should be able to use words properly.