What Airbus may issue is an AOT (Alert Operator Transmission). They could issue this if there is a technical problem that may be repeated. Furthermore they have in the past issued AOTs to remind operators to follow correct operational procedures. That they have not done so in this case is equally telling.
All manufacturers are acutely aware of product liability responsibilities (and lawyers).
Doubt Airbus would issue any document that could be seen as an admission to any culpability in the crash any time soon, unless it was something that was likely to happen again very soon (like some obvious problem in a recent upgrade to the aircraft). Lawyers for the manufacturer of the aircraft and the airline are contacted before the flight is even reported "Overdue". The lawyers work with actuaries and
PR people to figure out every move their client makes, when it comes to the crash. Even though an AOT might be the ethical thing to do, that only enters into it if the
PR people convince the lawyers, that it will help mitigate the damage to their client, and that would only be the case, if there is no doubt, that their client bares most of the blame.
This may sound cynical, but it's reality.