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The APIs are not restricted, but are now rate-limited to make inference of information like this very hard.

https://developer.android.com/guide/topics/sensors/sensors_o...

200Hz really isn't in the ballpark of making this "very hard".

IIRC the rate was limited because someone showed it could be used as microphone.

No permissions required to read motion data.

If I remember correctly, it might be necessary to declare the capability in a manifest, but there's certainly no prompt, nor a way to opt-out of an app reading motion data in the settings.

you can "opt out" using adb by revoking the gyro permission. some non-google androids also have the possibility of revoking it with the ui, or even going as far as to promt for it (graphene os)

GrapheneOS has a Sensors permission toggle to allow/disallow an app accessing sensors.