I just had a look, and no, Discourse app runs off an API and renders its own content, rather than just being a shell around Safari (or Chrome, or…)*
I, for my sins, am incredibly familiar with GDPR requirements, having worked with clients who must comply.
GDPR can be handled in a much, much, more subtle manner than the obnoxious cookie icon. I have got in trouble for criticising Discourse on this board, so I will just point out that by complying with one law - GDPR - it is not compliant with the European Accessabilty Act, in that it blocks page functionality…
* occasionally, I get asked to add SMDB as a desktop icon - if this is used it will launch in your default browser.