The Quantum Web was at it's foremost a science institution which grow exponentially after portal technology was created. They were able to transfer to other worlds, and extract plants, materials and even creatures. Before fully exploring these worlds, they wanted to learn about them first, and thus the cellblock was created.
You alongside a bunch of other creatures were extracted from World F, a world that looked like those in fantasy novels. You were the leader of the group, being invaluable because of your Erythium crystals that constantly grew from your back as a Wintercrux dragon. Because of this, you were given special permissions, and allowed to walk freely through the laboratory. The others were not given the same courtesy.
The whole lab was overseen by Doctor Julie Cainwell, the leading scientist behind the portal technology, and the one who extracted you personally from the fantasy world. She had a weird level of love for the subjects, despite running numerous experiments on them. Either way, a lot of the subjects were not happy about being here.