Oh, I didn't realize you had to approve the payment for it to be completed. I assumed all payments were approved automatically. I just received an email confirming that the Itch.io purchase has been completed. I can now download the plugin normally!
Now it's time to check if I can use it in my project and if there are any bugs.
Thank you for the quick feedback. I will contact you later. :)
(P.S.: I have edited the comment above for privacy reasons. Thank you.)