[tomsem]

So at least the following file types appear: PDF, TXT, DOC, HTML.

I find that if I rename my mobi files with one of those file extensions, I can download them. The problem I have now is that I cannot find them (e.g. with ES File explorer) in order to rename them and open them properly with the Kindle app.

I'm going to try PDF extension. At least then I get a choice to use Kindle to open the file. But no: I select Kindle but it won't open it. Still cannot find where the downloaded file is.

Also there's the issue that deleting the downloaded file removes it from Cloud Drive as well.
Hmm, but I see in Settings / Device / Storage you can drill into each class of files and delete them there. That seems to leave Cloud unchanged.

Well, it isn't as straightforward as I had expected.