I see from Mactracker that a new battery has a capacity of 205 mAh (38mm Apple Watch Series 1). For the MBP and iPhones I have used coconutBattery to show the decay in battery capacity over the lifetimes. Is there a similar tool for the watch?
No - neither is there a public API for apps to do this on any iOS device. Clearly there are private API (heres one version for iOS / not watchOS) and occasionally someone slips an app by review knowing full well that's against the rules - but they generally get pulled quickly or fail to work / crash.