Atmosphere nudging without external `p_mid`

`p_mid` is removed from nudging. However, in atmosphere nudging, we still need to use the internal `p_mid` to `perform_vertical_interpolation`.

Locate the atmosphere nudging code and the perform_vertical_interpolation entry point, then trace how p_mid is passed after its external removal. Confirm that atmosphere nudging obtains and uses the internal p_mid for interpolation without requiring an external value; the relevant validation path is not specified in the issue.

Written by the indexing model from the issue text.