I was just looking through my google drive and there's no trace of my whatsapp chat backups. Even after running another backup. And pages online confirm what you're saying.
I guess I'll have to use my GDPR rights.
Interestingly enough, there only is the possibility of exporting account information info, but the information page about that procedure explicitly says that messages are not included.
That's relevant because since there's no other procedure to export data, this means that Whatsapp is already not okay with GDPR procedures.
edit (2): I just sent an email to Whatsapp via their contact page (https://www.whatsapp.com/contact/?subject=messenger) asking for my data in accordance with GDPR. Let's see what happens.