However, when I enable storage management (backend --> easysocial --> settings --> storage (see screenshot)), users that don't have uploaded pictures yet (no profile picture, no cover picture, no media at all and fresh profilies) receive an error when trying to edit their profile data:
1048 Column 'size' cannot be null error
feel free to reproduce on my site. The attached user has no media so when using that user, You should be able to reproduce this error.
Keep in mind that You have to enable storage management in the backend first, before You can reproduce this error. I have disabled it for now so that new users dont run into this problem.