With 3rd party batteries it can't do this, so it doesn't (I think, will admit I'm not entirely sure exactly how iOS deals with 3rd party batteries it can't determine the status of), and if you replaced it with an official part then it would have been in good condition, so regardless which road you took, it's possible that you went from a state where the OS was clocking down, to one where it wasn't anymore.
The iPhone 13 Mini made up around 3% of total iPhone sales, so there's clearly a market for compact, mid-range phones ($600-$700). You can manufacture them in China or India for somewhere between $250 and $400, depending on the battery, camera, and overall performance.
The real challenge is that the retail price of a mid-range Android phone can't go over the $500 mark. People in developing countries are always stuck trying to balance quality with price. And for $500 bucks they expect a prime phone nowadays.
I currently have this problem (iPhone 11). It's not slight at all. Keyboard inputs sometimes has up to a full 1000ms latency and that's with autocorrect, suggestions, and spellcheck turned off. Scrolling in most apps are jumpy rather than smooth. When this phone dies, I don't know what I'll get. Hopefully a good linux phone exists by then.