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Perhaps Shocking Swerve, which is YMMV.
I don't know if we have a "series-wide" version of Wangst, but if we do, that'd be the one you want
EDIT: Crapsack World is close, very close
Edited by 4tell0life4 We can never truly eradicate the coronavirus, but we can suppress its threat like influenza
But I'm not thinking of Crapsack World, I'm thinking of a world that's supposed to be modern-day earth in a developed country, yet an improbable amount of horrible things happen to the characters. If the setting is explicitly such that you would expect all of those things to happen and it would be probable, that is just Crapsack World.
Still, We Have This I Swear
Darkness-Induced Audience Apathy can result from "this", but I don't yet know what "this" is.
We can never truly eradicate the coronavirus, but we can suppress its threat like influenza
When a show is set on modern-day earth in a developed country without any fantastic aspects, and yet there's a lot more suffering and death than is probable, particularly of the type that makes for a Very Special Episode. Like the main character's son has cancer as a child, and her best friend is murdered, and another main character has an abusive husband, and her kid's classmate commits suicide. Not the same as Deus Angst Machine or Trauma Conga Line because it's not about just in general one character that suffers a lot, but a number of bad things happening that, combined, are improbable for the setting. Especially tends to appear on soap operas and any type of Long Runner.