I don't think you can really blame the Kobo support for not answering your question: it's their official policy that users aren't supposed to replace batteries themselves, so they're not going to help you. I doubt Amazon would help you fix a Kindle, either. It sucks that devices are made to be thrown out these days, but that's how it is, and if we want to fix them, we have to do it ourselves.
Here's a Forma teardown:
https://www.ifixit.com/Teardown/Kobo...eardown/162028
Once you open it and find the battery capacity (apparently 1200 mAh?) and dimensions, you should be able to locate a replacement.