As of GraphQL Admin API and REST Admin API version 2022-10, information on application acting as the Merchant of Record for the order would be available through the Order object. This information would only be populated with supported applications.
merchantOfRecordApp field in GraphQL Admin API returns
OrderApp object and
merchant_of_record_app_id field in REST Admin API returns the id of the application .
Learn more about the Order object on Shopify.dev.