Thanks, but I already cleared the cache with no effect (only files related to ModuleManager in there either way).
Then I changed /site/modules/FiledtypeCropImage/ from the symbolic link that it was to be the actual files and now it's working! And the scales felt from my eyes, too...
For sure, a translation file called site--modules--fieldtypecropimage--fieldtypecropimage-module.json doesn't apply to a file physically stored somewhere else then /site/modules/FieldtypeCropimage/FieldtypeCropImage.module. Just didn't think about this thoroughly enough before.
So, for everyone running into this problem, too:
Don't try to translate a module that you just symbolically linked into the filesystem. It won't work!
Thanks for all your help here!
bfncs's post in Making a module translateable was marked as the answer