A guy i worked with a couple of years ago was writing web apps for ts3 but it was limited, only showed people online and allowed messages to be sent.
He also wrote a rental app that anyone could come and rent a ts3 server for 1-12 hours for testing at the end of this it would reset the users and passwords for the teamspeak server.
Not really sure why you would need a web app for ts3 now anyway they have a client for every OS Win, Mac and Linux aswell as mobile apps.
What specific needs did you have for it?