If you have Apple Care, I assume Apple will. They’ve done it before, but not on something this old. If not, there’s always DIY or 3rd-party.

They will still do it if it's below 80% on Apple Care, or $119 if you just want to do it out of plan.

You can do it yourself[0].

0. https://www.ifixit.com/products/iphone-13-mini-battery

Word of caution, it seems kind of difficult, I had Apple replace my iPhone 12 Mini and they broke the screen in the process (so got a free screen replacement too), so seems a lot harder than it used to be, think I did it myself back in the 3GS days last time and seems its way more brittle today.

I've replaced multiple iPhone batteries (just not this model), and the great thing about the iFixit kit is it comes with specialized tools you need and great instructions.

Indeed! And I bet Apple technicians have even better training, tools and reference documentation, despite that they broke my screen anyways! So I'll stick to my warning to ask people to be careful, seemingly really easy to break the displays in the process.