Problem finding books

Sorry if this has been posted before. I did do a quick search but couldn't find my issue, even in the Sticky.

I have some books that I purchased from Amazon several years ago which are in the Kindle app on my iPad 6. Somehow I acquired a different account over time which is now set up to manage my Kindle content. However, the old account uses an email address which is no longer in use so, long story short, I am unable to move those books to my new account and new iPad. Amazon were completely unhelpful and refused to merge the two accounts.

So I want to try and retrieve those books before I erase the old iPad in order to sell it. I have downloaded Calibre on my Mac and have successfully connected the iPad via the Content Server. However I cannot find the Kindle books when I look for them on the server in Chrome or Safari on the iPad. I can find other files, downloads etc. but no reference to Kindle or its books.

Does anyone know how to get it to see them and how to upload them to Calibre for conversion or storage? That way I can keep the books and not have to purchase them again. Hope the question is clear. Thanks!