Just replaced my Gear S3 battery (24$ + 10$ for tools). Excited to get 3+ days back. Links in comments, will report back with new battery life in a few days. : r/GearS3
Amazon.com: oGoDeal Replacement Battery for Samsung Gear S3 Frontier(SM-R760) and Gear S3 Classic 3.85V 380mAh Battery SM-R770,BR760,R765 EB-BR760ABE GH43-04699A Battery with DIY Repair Tools : Cell Phones & Accessories