My 15 Pro only had slight heat and battery drain when the 'Update finishing in background' notification was there in the battery status page. This was there for 2 days on beta 6 and 4 days + 2 days on beta 7 (after 4 days, it went away for a day and came back for another 2 days). I did not get the notification on beta 8 or RC and didn't have heat or battery life issues. Assuming that you haven't identified a particular app causing the heat/battery issues, maybe it's time to try the IPSW method or reset?
I don't think this is ever going to be fixed. I've been using the dynamic bubbles wallpaper for years and if you use it as the Home Screen wallpaper, it will only sync for 1 or 2 unlocks and then it stops syncing with the Lock Screen. Been this way since at least iOS 15 as far as I remember.