iOS lets you specify that accelerometer data should be recorded, and then allows you access to the recordings at a later date: https://developer.apple.com/documentation/coremotion/cmsensorrecorder
But, is there the equivalent for the gyroscope?
No, but of course you can watch the gyroscope at any time. The reason is that the gyroscope, unlike the core motion sensor, is very battery-heavy and doesn't even run unless some app asks it to.