Sourcing a replacement iPaq 3600-series battery

A few months ago I got a Compaq iPaq H3650, the same model that I had almost twenty years ago. This device left a strong impression on me, so even though I had (unfortunately) long ago gotten rid of my original one with a broken screen, I wanted to remember what these strange proto-smartphone devices were like. I got an iPaq on eBay for $10 (Pocket PCs are apparently not