Microsoft filed a patent for it, but so far, nothing has been launched
https://www.onmsft.com/news/microsoft-files-patent-new-surface-pen-rechargeable-battery
> So is there a Surface Pen with a rechargeable battery I can buy so that I
don't have to constantly buy batteries?
But maybe something like
https://www.amazon.com/Odec-AAAA-Batteries-Rechargeable-Battery/dp/B073PZWYB3
would solve your problem.