Hello Jonas,
Thank you for your response and sorry for the experience with login on the applications.
With help from the screenshots, it shows that the application is unable to generate a secure connection with the server to get you signed in.
Please help me with the below information:
1. Are you connected to any VPN
2. Have you tried switching the internet connection of the device.
Also, just try with installing any alternate application from Adobe from the App Store ( Creative Cloud for example) and check if you are able to login to it. If it logs you in, your account should automatically be identified by Acrobat Reader Mobile and Adobe Scan too.
Let me know if this helps.
Thanks,
Souvik.