On-device calendar exists?
The native AOSP calendar app was replaced by Google's own1. It went by the package name com.android.calendar, but is no longer found in either Google Play Store or on F-Droid (you can find its code on Github, though). As for synchronization, that's usually not done by the calendar app itself but by the corresponding sync service; most calendar apps use the "calendar provider" of the Android system to store their data.

If you want a "local calendar" that's not synchronized at any cost, and your device doesn't offer such, you can e.g. use Offline Calendar; but that app doesn't seem to be maintained anymore (last version is from 2013).



1: See Google’s iron grip on Android: Controlling open source by any means necessary