The batteries on original SE's are seeming to reach end-of-life now so I think I'll still have to jump to this. I've bought 2 used ones and had 2 new ones and they've all got dead/dying batteries.
If thats the only issue with your phone, aftermarket battery replacement service is pretty reasonable. 50 dollar ballpark and takes like 5 minutes. Just have a search in your area for phone repair shops.