(I initially wanted to edit my OP but I can’t seem to find a button for it. If I was supposed to edit the main post instead of posting a reply, please excuse me for that.)
After doing some more googling, I found this article which talks about changing some settings to Apache2 in order to make the .htaccess file be read: https://www.chalk-ridge.com/permalink-404s-response-is-not-a-valid-json-response/ I tried applying the mentioned changes in the apache2.conf file, sadly without any effect.
This seems to be the only article which is discussing this issue and also mentioning the JSON error. It also relates it to a website being hosted to a private server, so I am starting to bet the issue is somewhere with the configuration of my system.
Does anyone know more things I could try out to try and fix this?