It's a huge loss that otkazat'sya doesn't treat the Darkling sort of like a vampire, considering that he lives longer than most Grisha even under the guise of "descendants" and doesn't age at all, which should be very noticeable. This could have made his serious treatment more believable: he's not just young, but eternally young.
Look, I'm pretty sure I've read someone ask Leigh if the Darkling's a vampire. I'm pretty sure it was some time before Ruin and Rising was published, so it's not like that didn't occur to any of the readers.
... it was met by the usual mix of fascination and fear that greeted any mention of the Darkling.
“He’s not natural,” said Eva, another assistant; she had pretty green eyes that did little to distract from her piglike nose. “None of them are.”
Alexei sniffed. “Please spare us your superstition, Eva.”
“It was a Darkling who made the Shadow Fold to begin with.”
“That was hundreds of years ago!” protested Alexei. “And that Darkling was completely mad.”
“This one is just as bad.”
Shadow and Bone- Chapter 1
The belief in vampires (deceased people who in their lifetime had been sorcerers, bad characters, or murderers, and whose bodies are now occupied by an unclean spirit), which may be traced back as far as the eleventh century.
Slavic Myths and Legends (Jan Hanuš Máchal)
That could've been a decent start.
The Darkling so evil his unclean magic created Shadow Fold, upon death turned into even more unnatural creature, pretending to be his own descendant or spawning already tainted line that only serves to transfer the infernal entity the original one sold his soul to in return for power beyond imagination.
“Well,” I said, “there was an old serf who worked on the estate … He … he said that Darklings are born without souls. That only something truly evil could have created the Shadow Fold.”
Shadow and Bone- Chapter 5
The Black Heretic's asking to be viewed as a Faustian figure, and Slavic folklore's full of undead creatures.
Unfortunately we spend the whole trilogy in a head of a person, who's happily deaf to other people's bias, and her own are vaguely bland. Besides, the writer didn't bother with research and deeper worldbuilding. The term itself- vampire- eventually appears, but it's used to describe the Blight with no further details about said myth it's supposed to refer to. (That could've been connected with the Black Dracula's myth, when we're at it, since the original Fold was his creation, and these started to appear after his "final" death.)
... They’d had the same reports from other parts of Ravka: a blight that struck out of nowhere, a tide of shadow that enveloped towns, farmland, ports, each thing it touched dissolving into nothing with no more ceremony than a candle guttering out. In its wake, the blight left fields and forests leached of all life. Kilyklava, he’d heard it called—vampire, after a creature from myth.
Rule of Wolves- Chapter 3
To dampen my excitement further, not only I couldn't remember seeing the word before, simple search shows it's either incredibly obscure, or the author just made it up.
So yeah, Grishaverse folks are immensely superstitious, but that's just a word, like Alina's goodness or Nikolai's fairness. We have to come up with that superstition by ourselves.
edit: Hell, thinking about it, Alina's wariness of the Darkling could've been well-founded fear of a maiden facing a monster praying on those like her.