Unfortunately it has been confirmed to not be supported by an AWS support engineer here: https://repost.aws/questions/QUgXvyCDowSvey_vDeuxAsXw/cognito-customize-federated-authentication-request#ANnanO3BZkTKKAMtKFtf53SA

But also says:

Having noted the above, I can confirm that an existing feature request is in place with the Cognito Team, to add support for this feature