No, most sites have a button stashed in some submenu of the account page that allows you to request your data. It’s either a legal requirement of the GDPR or they just don’t want to deals with individual email requests, I’m not exactly sure.
It usually does take a lot of time for the request to be “processed”, you usually get an email with a zip archive after about a week. I’m not sure if that’s malicious compliance.
You can also send a GDPR request to have them delete all your data, but they do have 1 month to comply and in my experience most services do take that long to “process” your request.
Keep in mind that many services hide these options for non-EU citizens.