More users of older iPhones are now claiming an improvement in performance after a battery replacement. One posted a couple of screenshots on Twitter showing the CPU being underclocked to less than half of its stock speed before returning to normal after a new battery was swapped in.
https://www.notebookcheck.net/More-evidence-of-Apple-throttling-the-CPU-in-iPhones-with-worn-batteries.273072.0.html