On the default setting, Amethyst should run less than a minute on the background. But the phone can force it to stay open in those battery settings. 

 Extra strange. This is with background usage disabled 🤔
https://i.nostr.build/eBunNcuirX85xTd2.jpg 

 I have a pixel 8 as well and mine doesn't do this. I am not really sure how to reproduce it 🤔 

 https://image.nostr.build/6ff38cf145d177e9f0d5e8d518df3ec44b60631d69027b373b60207e60720467.jpg 

 I'll try reinstalling Amethyst and starting fresh.