Hey,
I have since found a sollution that works for me, so I will share it and add the steps I took to get there.
Firstly, my version of Acrobat Reader DC was the Croatian version, I did not write down the exact version, but it was updated fully using Check for Updates and with Repair Installation. I downloaded this version from https://get.adobe.com/hr/reader/ where it does not give you options to choose and I assume just downloads and installs the version from your local region or country. I could not get this version of Acrobat Reader DC to work with Document Cloud taking all the steps described above.
What I did was uninstall Acrobat Reader DC using windows "Add or remove programs" and using the tool "AcroCleaner" removed any previous data or profiles I could find. Next I found a link where you can choose which version of Acrobat Reader DC you want to download: https://get.adobe.com/hr/reader/enterprise/ ,
here I chose:
1. Windows 10
2. English
3. Reader DC 2021.001.20145 English for Windows
With a file size of 181 MB
Unlike the first download attempts, where you download a small file that after running it sets up and downloads the rest automatically, this was the full file size installer.
After running and installing this US version, immediately upon opening the app I could see the buttons and options for Document Cloud, even before loggin on my account. I now think before I reinstalled Reader that I was using the english version back then as well, but honestly never paid much attention in what language the UI was.
So my advice to anybody else with this problem is to try and use the English version if you, like me, had a different language installed. I don't know if my problem stemed from it being the Croatian version, but it was what fixed it in the end.
Good luck to you!