I also wasn’t able to register an old K3.
Two-factor authorization with phone didn’t kick in at all, so I couldn’t add this OTP to the password.
Anyway, here is what I do and suggest you the same:
1) Download and install Kindle for PC, version 1.17. Open it and immediately uncheck autoupdates in the settings.
2) Install calibre and a plugin for it called “DeDRM plugin”.
3) Login to Kindle for PC with your account. Then download books you need. Go to Documents/My Kindle Books folder, sort by filetype. Drag and drop the book in azw format to calibre.
4) Now your books you bought are in the calibre, deDRM’d. Now just continue from calibre and connect your Kindle to transfer books.
Enjoy reading!
P.S. K3 is also a powerful audio book reader
just put mp3 in documents or audible folder on Kindle and they will appear in Home page as usual books.