Thanks for your help, Mark!
Removing cleanly and reinstalling Redactor and ContentBlocks works now. You were right, it should have been a licence issue.
Replacing the Administrator policy on the web context with the standard Context policy is useful, but unfortunately has not brought anything.
Now I could break it down to Redactor. If I uninstall it, non-sudo users can see the new-resource-form. If I install it, I still get: An error occurred… Access denied.