Just to keep everyone updated, we did get a response from the Teamspeak team. Here is what they said:
Thank you for your interest in TeamSpeak. Currently the beta is closed and only available for registered participants. As we work through our list of beta testers, new invites will be sent out to randomly selected beta registrants.
Please note though that occasionally there will be a few codes posted on our social media.
So please make sure to follow us across all platforms.