I had a lot of issues with Amazon media. I have a .co.uk account, but had to switch in the end to .de to access the full range of media (Books and TV via Prime). It then got very confusing as to which account was linked to my Kindle and my TV. I spent a loooooong time on the phone to Amazon (after working my way through various online layers of Customer Service), where they eventually set my home location for all digital media to be Switzerland. This means I have very limited access via my .co.uk account to Digital media, but can still order stuff physically. The .de site has nearly the same offering of English Kindle books as .co.uk; ironically they are often cheaper as well! Good luck….

you have to buy the books in the shop of your Kindle account. In other words: you are registered on amazon.de, then you must and can download the English books there. The library of purchased books does not sync (at least for me) between .com and .de account.

I use an both uk and de accounts without issues.
The only thing i did is, purchasing on my phone/pc
and it dowoaded to the kindle later
never actually purchased through the kindle itself