iPhone SE (1st gen) - battery replacement or buy a new one?

Hello! I have an iPhone SE (1st gen) that I purchased in 2016 or 2017 (I think). It's working fine but the battery is now unreliable. I've had many unexpected and sudden shut-downs.

I was wondering if I should replace the battery or buy a new one. I can't afford the newest models, so I'm thinking of buying an old refurbished one (maybe XR or 11).

My concern is whether it is worth continuing to use SE (1st) by replacing the battery? I know it's ancient but I don't need fancy functions so it would do the job for me. But I'm worried if it won't keep up with the iOS update etc. Is there any risk that it wouldn't be protected or anything in the next few years?

I like the idea of keeping the cost minimum by simply getting a new battery, but if it doesn't last me for another few years then I might as well get a new one - then I can probably get more data on the iphone, which is never a bad thing!

I wondered what other people might do in my situation? Thanks in advance!