Clock does not update

I had this problem with one of the earlier watchOS 6 betas as well - it turns out that it was syncing music playlists from my iPhone. I had never enabled that, but, one of the betas apparently did, which prevented a second beta from being able to be installed. Check on the watch under Settings -> General -> Usage to see if this is the same for you. You can disable playlist syncing in the Watch app on your iPhone.