I agree with Julius, I had the same issue on MacOS 13, and continues on 14.
I requested my serial as well, and I got a mail referring:
"You can see it below, along with a download link, if you need to reinstall the associated product you purchased."
And there's no link in said mail. Which is interesting. Is the paid version a different download than the free one? or can a valid serial be entered in the free version to upgrade to Pro?