hello!
heres a guide to replace you surface keyboard battery https://www.youtube.com/watch?v=iOy9HwEXMO8 you should also note that that swollen batts are dangerous, and you should take extra precaution, and this device is pretty hard to repair, with a rating of 1/10. just be extra careful!!
heres also the replacement battery: https://www.ebay.com/itm/144807286325
hope this helps!^^