Copyright can only be waived in the US by dedicating the work to the Public Domain. In most other countries, it can only be assigned or licensed to someone.
The “standard practice in all forum software since practically forever”, has been to include a very broad use license on the work, without switching the copyright holder, in order to protect the forum owner from liability.
The GDPR is about a very broad take on “privacy”, where the rights of “access, modification, and removal” get extended to any “personal information”, no matter whether it’s “personally identifiable” or not.