Apple does battery replacements on them for a reasonable price. Might not be worth it for a phone that old. But it is nice that Apple keeps updating devices until virtually no one is using them anymore.
Sorry, excuse me while I go burst my sides from laughter. Apple does battery replacements for more than a (entry-level, admittedly) new phone costs. And that new phone includes a battery. ;)
Moreover, Apple refuses to do battery repairs if your phone has other problems, even if those problems have absolutely no relation to the battery, like... a cracked screen. (I'm not kidding, but hey, props to them for actually being honest[1] for a change. That's a refreshing surprise.) Personally, I know very few people with Apple phones over a year or two old who don't have a cracked screen.
[1] https://support.apple.com/iphone/repair/service/battery-powe...
Replacing the battery with a smashed screen is almost impossible without also replacing the screen because you need to use a suction cap to pull the screen off. If it is smashed you need to scrape off all the chunks which removed what is left of the screen. These days the glass on the iPhone is much stronger than it once was so I don’t know anyone with a cracked screen.