The TS6 server files that are required to utilize screen share are available for self hosting.
This will be coming out for users to self host in the near future, however there are other ways to try it out.
They have are now released and can be downloaded for self hosting:
https://hub.docker.com/r/teamspeaksystems/teamspeak6-server
You can currently use screen share via Peer-to-Peer in Group & Private Chats, and also on our Official Community Servers which you can find on the dashboard in the new client.
Another option is to host a TeamSpeak Community, which is our hosted solution.