It's worth looking over the full list of indexed fields for authority records, here in the docs:
You'll note that, within the authority records index, the Identifiers for Corporate bodies field is indexed as: corporateBodyIdentifiers. This is not being included as a foreign type on the archival descriptions at the moment, so attempting a global search like:
Will likely return 0 results. However, the same query run in the dedicated authority record search box should return records that have a corporate identifier
Because it's not indexed as a foreign type on descriptions, I'm not sure I can provide you with an ES query that will return, for example, all descriptions that are linked to an authority that has a corporate identifier. It may be possible to craft something like that with SQL - that would take a bit more investigation.
However, the fields you are trying to search on, as far as I can tell, don't actually exist in the index - which is why you are getting either all results or no results.