It all centre's round having one and only one person responsible for the whole flight. And that's the Captain of the ship.
I don't know or have flown an Airbus even in the sim.
There are usually multiple different ways of seeing if the gear is down by lights in the cockpit. The pre FBW days we used to have lights which there was two bulbs in each socket. Then we had a back up panel which also used to have lights that was linked to a separate set of micro switches and on a different bus bar.
FBW we again have multiple sensors all feeding back into the landing gear and steering computers. Note the S there is more than 1. This then displays in all sorts of places and you never loose until the very last screen die's including all the radio controllers. And even if all the screens die which is something like 7th twig in the failure tree the alternative gear extension will still work off the direct battery bus. All of them its just a switch to a computer. in fact in this case if they had gone for the alternate it would have come down I suspect.
But fundamentally your bum and the aircraft performance knows if its come down or not. Single leg unsecure is a bit of a bitch. But all up not moving when you have selected down you should know about. You feel the up locks coming out, you feel the drag while in transit, you see the airspeed drop, you then feel the down locks engage, you feel the doors close and the aircraft speeds up again. Having 2 legs down V 3 makes a huge difference to how the aircraft flies due lack of drag.
The memory item is don't put the gear down above the max extension speed. Nobody has a clue what they did
The taking off again has actually worked multiple times over the years with other types, even props. And they did a circuit and landed with there pride, aircraft and runway broken.
With these engines and the placement of the fadec and permag alternator to power the fadec it is definitely better to stay on the ground.
As you can see on this pic of a NEO engine you have a whole load of fan to scrap away before you get near anything else.