They have asked the US to allow the BA codeshare and said this about the UK ACO.
When the Joint Applicants submitted their application on December 9, 2020, they anticipated the CAA would have issued all required licenses and authorizations by now. However, although the CAA has assured Aer Lingus (U.K.) that its application remains on track, those approvals have not yet been granted but are expected to be issued before the end of May
https://www.regulations.gov/document...2020-0250-0007