This might not be a very pirate thing to do but I cancelled my Kindle Unlimited when I found out I could get all of them, for free, delivered to my Kindle app, from my city's library via Libby. Books, graphic novels, audiobooks, manga, and more, just there for the taking.
Libby (Overdrive) was sold to the Private Equity company that debt loaded and then bankrupted Toys 'R Us while giving their execs big money. Simon & Schuster books are also being sold to the same group. Since they took over Overdrive they've removed the easy ability to recommend books to your local library that you would like to see them buy for you, it'll only get worse from here sadly.
That said, I too am using this function quite a bit as well.
This is why I chose to go with kobo over kindle. You still have overdrive/libby access, but can also import and organize all of your books via calibre.
I moved from a major metro area to middle of forking nowhere several years ago. I kept my library cards from the metro area, which still work for Libby ebook and magazine downloads, while the local rural library is tied into a regional system for the occasional dead tree book.
It is still possible if you have an old enough Kindle. I have a 1st gen paperwhite and can just connect it via USB to my PC and pull books off the kindle with Calibre and then remove the DRM.
Though if you're wanting to remove DRM from Kindle Unlimited books, you'll have to actually edit the DeDRM plugin code, as by default its set to not let it be run on KU books.
I had mine jailbroken and had koreader on there. I put it online without realizing and amazon forced an update without my consent so they could patch that little loophole. It still lets me download azw3 files from content & devices to "manually transfer to device" but I was not pleased
Kindle 7th Gen is capable of the KFX format, it's likely to have received an update recently because the KFX format has a new and so far unbreakable DRM. The NoDRM team appears to want nothing to do with it. Kindle Unlimited books are generally served in the latest formats because they monitor how much of the book you read and pay the author per page.
If the books are already downloaded and are in AZW, PRC, or Mobi format it's likely, but not guaranteed, possible with NoDRM/DeDRM_tools plugin on GitHub.
The only way to do it now is to have an older Kindle device attached to your account, you can go into "Content & Devices" and you have the option to transfer to your Kindle via usb. Which will give you an azw3 file that you can use with DeDRM. But you can't do it with KU which will only be served in KFX format.
The KFX team have infiltrated the groups who come up with vulnerabilities to allow DRM removal of kfx to then patch those issues before they can hit the general public. They've done it repeatedly so far so that's why they've given up on DRM removal of kfx.
I don't remember the steps, but there used to be a way to do it through Calibre. You could download your library into the Kindle desktop program, run a DRM removal tool, and have them available through Calibre.
You might have had to remove the DRM through Calibre, I'm not sure. Hopefully this gives you somewhere to start though :)