I downloaded the update this afternoon and everything is now back to normal. The Health and Activity apps have their data back — and not just the data from before the 10.1 update. The iPhone continued to collect and receive Health and Activity data during the period of the bug — even the weight data I entered manually. It just couldn’t display it.
This must have been a simple fix, like a typo in the code, if they could go from gathering data to releasing a solution in two days flat.