The Mediawiki-based API is not sufficient for reconciliation
Thanks for adding me in the loop! @RazShuty, do you mean any of this?
- migrate the existing reconciliation service (https://tools.wmflabs.org/openrefine-wikidata/) to work on any Wikibase install
- create a Wikibase extension that already provides a reconciliation API natively, without having to create a wrapper like I did