For the last 2 version (18.2 beta 1 and 18.2. beta 2) I haven't been able to successfully update to either of them. I have been running Sequoia on an external drive for testing purposes and didn't have this problem with any of the 18.1 versions.
I'm currently on 18.1 (public) and when I download the update for 18.2 beta 2, the update appears to run (takes about 30 mins), preparing update, the restarts. When the Mac restarts, it just boots straight back to 18.1 without having applied the update.