Yes, but it is a bit unusual for a “beta” to be the stable version, when there is a such a thing as “stable”. Beta is normally taken to be a testing version, between alpha and stable releases. But it shows we can’t just go on our own assumptions about what alpha and beta mean.
No they don’t have a central managed hosting, and that is the point they are making. It is intended for someone to host for their family and friends. There may be some hosting it at various places but no central list you can find them on. Those sites, of course, will federate with other Fediverse networks, but no-one will necessarily even know they are GoToSocial nodes.