> it uses some that battery API as a heuristic for a lower-power version of the site?
As a naive user I would expect websites to not be able to receive information about my battery state. With that information they can track my mobile phone usage pattern, and with some cross-referencing gain even more specific private information.
Totally spitballing here. Strava being a website that requests battery does not seem wildly outlandish to me, albeit it is a bit suspicious in general.