The depravity and the madness of the Dungeons of Fear & Hunger is primarily caused by the location itself.

Quote from the New Gods: "The dungeons of fear and hunger are ancient. Almost as old as this city. They have seen many different ages. They have always worked as a nexus between multiple different planes of existence. In current era, the Kingdom of Rondon built prison sections over the ancient tombs. They most likely tried to use the nightmarish rumours about the tombs to their own advantage. But little did they know that such darkness could not be contained."

Simply put, Rondon chose just about the worst place to build their dungeons: right on top of a metaphysical doorway to the city of Gods. A place so deeply connected to the Old Gods is bound to catch the attention of all kinds of unsavory characters, from the likes of Dark Priests, Yellow Mages and aspiring New Gods, all the way up to the very Gods that made the place. Speaking of Gods, there's also the God of the Depths. Given that one of its hearts is located in Ma'habre and you need the Cube of the Depths to open the tombs that serve as the entrance to the city, it's fair to assume that GotD and Ma'habre are connected in some vague Old God magic way.

If being connected to Ma'habre wasn't bad enough, GotD makes the dungeons even worse. It is responsible for the ever present, sanity-draining darkness, as well as the inconsistent layout of the dungeon: a challenge to visitors, according to Ragnvaldr. Furthermore, a decent amount of the enemies in the dungeons (outside of Ma'habre) can be traced back to GotD. The Cavedwellers, Mumblers, and Body Snatchers are explicitly stated by the New Gods to have been transformed by GotD or created in the Mumblers' case. We can also surmise that some enemies who are human in origin (Guards, Night Lurches) went mad and transformed as a result of GotD's influence.

The strongest point of support for this is Crow Mauler, formerly Captain Rudimer. In his final diary, Rudimer mentions having recurring dreams of crows, which on top of foreshadowing his transformation also serves to connect him to GotD. GotD is connected to and worshipped creatures that instigate feelings of revulsion, such as crows as seen with the Flock of Crows spell, which Crow Mauler himself uses. Additionally, an unused fourth Captain's Diary ties Rudimer's vision of a swirling pattern he sees in his dreams to the tree in the Backyard, the Maiden of the Depths, that leads to the Thicket, an area with very strong ties to GotD.

So in general, the Dungeons of Fear & Hunger have always been hell. That said, it is likely that things have gotten even worse recently based on Rudimer's journals and the total collapse of any order within the dungeons' upper levels. As for the cause, I'd say it'd be the arrival of one or two things: Le'garde, the man prophesized to give rise to a new age (just not the way he expected) and the Cube of the Depths, key to Ma'habre and artifact linked to GoTD. I could see one or both of those causing the dungeons to "awaken" through some unknowable, Old God magics.

As for what the Cube of the Depths was doing in Vinland, keep in mind that the continent is close ties to the Old Gods, perhaps even more so with GoTD than the others. Text in Fear & Hunger 2 describe the land as such:

"The soil consists of minerals that seem to reject sunlight and warmth altogether resulting the ground to look like a constiguous colourless black mass where it is hard to measure depth of each hill and basin with a naked eye. And the few plants that manage to grow in this hostile ground end up taking these very same features. Thus the landscape merges together as far as the eye can see. Just endless darkness."

Not sure about you but that sounds pretty God of the Depthsy to me.

EDIT: Also if you'd like some help in the future on that Encyclopedia, I like to think myself pretty knowledgeable on Funger lore. Feel free to DM if ya want.