It just so happened that we ordered a taxi the next morning to the airport from Mac, the internet was not very good there and they closed in 15 minutes. It seems to me that the only taxi is without prepayment and card entry. By a ridiculous coincidence, I sent 5 requests, as it turned out later - I was "checked" by mail and Whatsapp message, but I did not have the opportunity to respond and confirm.
Despite the whole described sur on my part - the car arrived, the driver called me and everything ended well.
Thank you for your trust and help in our situation.