Poor
Can I ask you to keep following up and post back here?
Maybe collate the mails you've received from both parties, and send it to both and try to get it escalated.
It may seem a petty thing, but I've had the same in the past - leaving the lounge at "gate open" or early stages of "boarding" then suddenly seeing "gate closed" when on the way, rushing in a bit of a panic, sweating, elevated heart rate etc. only to find boarding hasn't even started - not the best way to start what can be a long journey.
"Relax in our Galleries lounges before a panicked sprint to board the flight with a mild case of stress"