My original HomePods are on the official Beta program.The OG Homepod does not have access to the official developer/public beta program. Only the 2nd Gen Homepod and the Mini do. For installing audioOS 17 beta on an original homepod, you´ll have to manually find and install the prive "invite only" dev profile.
In my opinion, is not worth it. The unit could get brick or die like in past beta firmwares.