it is possible the engines continued to run...but at reduced thrust
I think the engines continued to turn and possibly produced some thrust, though insufficient to maintain level flight or better.
It is something to consider, as the plane appeared to be under control with hydraulic pressure to run the flight controls.
I do have to wonder if somehow the FADEC system tried to protect the engines a bit too much.
I remind people that in addition to all the problems, the plane landed with about a 10 knot tailwind.