IDC: Factor functionality out of main Jetpack class

We've added a decent chunk of code to the main `Jetpack` class. For our own sanity, as well as for future developers of Jetpack, let's factor that code into a separate class.

We can factor methods like `sync_error_idc_validation()` and `check_identity_crisis()` out of the `Jetpack` class and into a new class like `Jetpack_IDC`.

This should make discovery of the code a bit easier, since we've got better naming and encapsulation, and should make it a bit easier to test.

Locate the main `Jetpack` class and inspect `sync_error_idc_validation()` and `check_identity_crisis()`. Factor the IDC functionality into a new `Jetpack_IDC` class with clearer naming and encapsulation, then verify that the functionality remains available through the existing Jetpack behavior and is easier to test.

Written by the indexing model from the issue text.