I just updated to Version 13.0 Beta (22A5286j) running in a virtual machine on an M1 Mini. It too said there was an update after updating but then after it checked it said everything was up-to-date.
(note: It doesn't explicitly say "Beta 2" but rather it gives the build in this case (22A5286j))
Topic:
App & System Services
SubTopic:
Core OS
Tags: