I think no matter your carrier for unlocked version it should end in XAA in order to qualify for beta. So mine is Xfinity mobile and it is CCT/CCT/XAA if last 3 end in VZW or ATT you are out.
I don't think the network matters. If you're in an unlocked model S10 you should qualify for the beta. The version branded one will not. If your phone has a boot up screen that had a Verizon logo, you're out of luck.