From what I understand, all posts currently made on the Beta will be gone. Once it is ready, the final mitigation from all content will happen and the forum will transition to the 'new version'.
How will the mitigation to the new forum be done?
The same way that it is being done now (the topics/posts up until a certain date are there).
Should we already now register in the beta?
All accounts have been transferred, you just need to reset your password there.