Notes about investigation:
The fact that Index: is a custom namespace (different names whithin the wikis, different IDs) is currently a problem. Cognate is not ready for that (same problem occurs with custom namespaces on Wiktionary) and the database structured should be modified to make this work.
This is not impossible but will need further investigation, finding the IDs of the Index: namespace on all Wikisources, changing the database structure and repopulating it, before finally deploying Cognate.

This is not impossible but will need further investigation, finding the IDs of the Index: namespace on all Wikisources, changing the database structure and repopulating it, before finally deploying Cognate.

An other possible way of solving this issue is to move forward on task T74525 that is planning to harmonise the Index: namespace id between Wikisources. The Index: namespace ids are currently stored in the $wgProofreadPageNamespaceIds configuration variable.