Aaaaand here I am again, continuing my monologue.
I've now moved my settings from modules.d/suricata.yml and modules.d/system.yml into filebeat/filebeat.yml. That allowed me to run the setups for both system and suricata without any errors. I also ran the full setup via sudo filebeat setup -e and got no errors.
However, the Kibana dashboard still shows nothing.
The discover page is also completely empty
I'm absolutely out of ideas and patience.