Getting assets from an entry programatically
In the returned object I'm expecting to see an array somewhere for custom field values listing the asset Id's, but it's drawing a blank

The reason for this is that entry fields are lazy-loaded, meaning Craft only queries the values from the database once you access them using their field handle (or execute the entity query you get through the field handle, like with the asset field). You can change this using Eager-Loading.
Without eager-loading, to get the asset you need to use the field handle (featureImage, in your case) to get an AssetQuery. Then you can use that to get the images (assets) in your field.
$entry = Entry::find() 
  -&gt;slug('0002')
  -&gt;one();

/** @var \craft\elements\Asset */
$featureImage = $entry-&gt;featureImage-&gt;one();

$featureImageId = $featureImage-&gt;id;

See Working with assets field data and Querying assets. The object returned by AssetQuery::one() is an instance of \craft\elements\Asset.