Wouldn't that much speed cause the plane to ascent naturally, even with zero pitch, just by the body lift? (Although, it is quite possible that real life planes have negative body lift, I have no idea)
I believe that while smaller planes will naturally pitch up as speed increases, jumbo jets are much more lumpant even with the correct flaps. That's the terrifying thing in my understanding: the plane basically had no manual pitch due to incorrect config values, and were barely gliding off the ground from minimal natural lift. Meanwhile the two potatoes at the helm were fiddling with the config values instead of pulling on the yoke.
If there’s more power than needed for the trimmed speed, the airplane will climb. If there’s less, it will descend.
262 knots is well within the trim range, so it’s impossible to say without knowing the trim setting, but if the airplane was programmed to hold an altitude at 262 knots, it could (by driving the stab angle of incidence higher or lower, as needed)
The flight director did the right thing — displayed how it would manage level flight
The pilot did the wrong thing - copied the misconfigured flight director instead of flying the plane