I replaced iPhone batteries in family and friends phones more than 20 times. It's only about $15 and 10-20 minutes of work. Some after market batteries don't last year even a year, some are good for 2 years.
I actually got it serviced at an apple store, and coincidentally they only had one 1st gen SE battery in stock at that time.
I don't think the battery was bad though, but instead the new iOS version being more power-hungry given the new models and chipsets coming out every year. The new battery was already at 92% health only 4 months after it was installed, which was a bit surprising for me.
At this point I just accepted that it was at the end of its lifespan.
Only once I bought original Apple battery, it didn't last even a year. I suspect it was made at the time iPhone 6S was in production so battery was waiting at the shelf for many years. It is probably the same case with you SE, Apple no longer makes batteries for 1st gen SE, only using what was made years ago. Old batteries, even not used, don't last long.
I don't think the battery was bad though, but instead the new iOS version being more power-hungry given the new models and chipsets coming out every year. The new battery was already at 92% health only 4 months after it was installed, which was a bit surprising for me.
At this point I just accepted that it was at the end of its lifespan.