Optimizing battery use on a Nostr mobile app is hard. It’s one of the things we are constantly working on with nostr:npub1pu3vqm4vzqpxsnhuc684dp2qaq6z69sf65yte4p39spcucv5lzmqswtfch. I know nostr:npub1xtscya34g58tk0z605fvr788k263gsu6cy9x0mhnm87echrgufzsevkk5s has done tons of work on performance and energy usage with Damus too.
To be fair, the nostr web apps often use tons of cpu cycles, we just don’t notice as much because we’re more likely to be plugged in and not held in our hands.