The entire wp-content folder seems to be in possession of www-data and I have at some time applied chmod -R 777 to the whole folder (No need to tell me that this is not secure).
Seems to be — means you will need to check if this is really the case. It may be not true.
BTW, I saw really bad designs where CSS files are out of the wp-content folder. You need to check where are these CSS files again.
Your browser may provide you the feedback of the exact location if you inspect.
Further, you may have used the plugins that alter the position of wp-content folder. If this is the case find out where is the new wp-content.
Consult SO web site and get the error log on your Debian web server to understand the possible problems. The errors may be dependent.
You may have some bad configuration in your .htaccess or other settings may forbid opening your CSS files.
Probably 10 more reasons may cause this problem, but hopefully this may be a good start.