I'm having the exact same battery issues as the others. Had my SE just over a year and had my first unexpected shutdown with 13% remaining. Battery still has 91% original capacity. Overall the phone runs silky smooth, but I'm definitely not getting 3 days of battery life anymore. Debating on paying $29 for the new battery...
I don’t think it’s the battery, it’s iOS 12. At least for me. Phone is brand new and was made in August 2018 with of course 100% battery capacity. It ran fine with long battery life on iOS 11 for the week I had it on that.
I guess it’s worth a try for you with your battery being less capable, but every time I’ve had Apple work on my device it’s been damaged or not reassembled right. I had them replace the screen on my 5S and it was returned with the screen adhered wrong and bad light bleed from pressure on certain parts of the screen.
Not worth the risk to me, but this battery life is tough to get by with. And of course it’s putting unnecessary charge cycles on the battery thus wearing it out faster.