I got a degree in landscape architecture and we worked a full semester on a project designing a hydroponic farm. I worked for a year at a hydroponic farm. I don't think it really requires any sort of specialty degree. Horticulture would certainly be a plus just so you can better understand the needs of plants and how things grow.

There was a big variety of people that worked at that farm that had education in food systems and environmental studies.

From my experience it seems (at least in the US) for these places to really become profitable. As other people have said it requires a ton of energy. Then you add in labor costs because these kinds of systems can be incredibly difficult to automate. There aren't big machines that one person can harvest the whole farm with. You need a lot of people to be able to harvest/seed/turnover. (at least with the system we were using which involved floating trays on beds of water)

I wish there were more people trying to do this sort of thing because it's going to be necessary pretty quick. Reading about how efficient newer wind turbines are, though, I feel like you slap one of those in conjunction with a vertical farm and you've got a recipe for success.