To update to beta you need to change this lines:
version=$(curl -s -S -k https://repo.teaspeak.de/server/linux/amd64_optimized/latest)
requesturl="https://repo.teaspeak.de/server/linux/amd64_optimized/TeaSpeak-${version}.tar.gz"
Use a updater script ;)
You can find one here: https://forum.teaspeak.de/index.php?threads/linux-how-to-update-your-teaspeak-server-including-script.86/
And for use beta you just need to edit the script.