So, working with 4Km2... There are 13 million square kilometers of arible land on earth: https://en.wikipedia.org/wiki/Agricultural_land . If the virtical farm is strung up with 400 meters of 10cm layers, that makes 4000 layers. That would be 16 000 square kilometers of farming area, or a bit over 0.1% of all arible land. I think that with modern vertical farming, using a 24 hour year around light source, the farming surface can produce several times the avarage arible land production. Lets say 4 times... That would make almost 0.5% of the world farm production in just one tiny area. So it would take just 200 such constructions to replace tradtional farming entirely...
If you have 4000 layers, you need 4000 times as much light, so you need a 16000km^2 orbital mirror focusing on your farm's elaborate set of light-pipes. The highly focused light, like a CSP plant, would ignite birds that flew into the beam. At that scale it would probably alter the local climate, given the amount of heat transferred to the air.
That is not how aquaponics and vertical farming work. They use solulable nutrients which are either gained through a nutrient cycle (the water flows down to a pool which has fish in it), or via mining of otherwise hard to get nutrients. Soil is not used. While the source of all these nutrients is a problem, it is comparible to the huge quantities of petrolium based fertilizers that we use today. It is bad, but what we have now is bad too...
... so you are proposing a bad idea that seems pretty wrong from multiple aspects. generally hydroponics is a sht cheap substitute for real growing for those who cannot afford quality vegetables (sadly, I sometimes fall down that hole too and then regret this decision while eating this tasteless cr*p full of unhealthy chemistry).
A 4km by 1km parcel of land is not large for farming. But put vertically, it represents the biggest open cut mines ever made.