As far as I know (and I’m not 100 % sure), no. You don’t even need to inform users that you use functional cookies. Most likely because these work for the person using your website, not against them (persisting the session, settings, and so on).
The GPL licenses were all written by the free software foundation for the GNU project. But that doesn’t make it less worthwhile to contribute to this cause, too :)
Das „free“ in „free and open source“ hat tatsächlich wie bei „open source“ nichts mit dem Preis zu tun, sondern steht für freie Software.
Falls allerdings für die bezahlten Funktionen nicht ebenfalls der Quellcode veröffentlicht und Modifikationen und Vebreitung erlaubt werden (was möglich ist!), wäre es weder frei noch open source.
GDPR wasn’t what introduced cookie banners, that was the ePrivacy directive which came before the GDPR. Either way, I’d argue cookie banners are an act of malicious compliance with both of these, as I’m pretty sure they were intended to reduce usage of tracking / analytics / other non-required cookies altogether. The annoying banners are, in my opinion, an effort to make people angry at the EU instead of the ad companies.