Another option is to get a battery replacement kit from iFixit.[1] I did that and it doubled my SE's battery life.
1. https://www.ifixit.com/Store/iPhone/iPhone-SE-Replacement-Ba...
The battery page in settings, under Battery Health should tell your capacity and other info. for me a new battery fixed everything... and batteries aren't usually covered under warranty as far as I know in general but Apple replaced it for me. FedEx Overnighted it to their repair center in California, and then back. So only without a phone for a few days. Kinda like a brand new phone just by changing the battery.
I know the OS itself prompted me to get a repair. Got a popup when restarting about a unexpected shutdown. So maybe that helped with the replacement process.