at first I noticed increased battery drain after updating to android 13 on P6P. I was looking around in the app settings and i think the update reverted some application setting to the default. I went to
Settings>apps>(insert app name)>battery
and selected restricted on all apps, except for a few things like signal or my mail application that i want notifications for. I also disabled background data for every app except signal and a few others. After doing that my battery life has increased tremendously, there is very little battery drain. I'm happy that theres minimal activity in the background, which is one of the reasons I wanted to switch to GrapheneOs. To be able to dictate what app has what permission individually is an awesome feature. I hope this helps!