What I'm looking for is something like what Laeta Kalogridis's Altered Carbon did with the main character. Basically, someone who's good at fighting/magically powerful (if it's a fantasy, of course) gets woken up. But I'm looking for that they don't just wake up, but someone wakes them up with a job to do. The only thing I've read about this is The Destroyer, here on RoyalRoad. I am leaning more towards Sci-Fi for this request, but I am fine with any genre.

Going purely by the literal definition of your request, Invisible Werewolf Dracula meets Vampire Mummy Frankenstein fits the premise perfectly and is sci-fi. You haven't lived until you have seen a chase scene with werewolf cyber-cops.

Similar to Laeta Kalogridis's Altered Carbon?

I would recommend Richard Morgan's Broken Angels and Woken Furies. Especially the latter.