Why is the barometer on the phone handled by the fitness shit? If this is legit the reason it wants health and fitness permissions, the sensors should just have their own permission category, IMO. Or you know, just have everything piecemeal so the app only uses what it actually needs and gets nothing more.
The barometer is one sensor in a package of sensors that includes the health and fitness-oriented sensors. The permission grants access to the sensor package.
It isn't related. The manufacturer of the sensor package realized they could put a barometer in the package at a smaller cost than what they could charge for having added it, so they did. There's no conspiracy except for the usual profit hunting.