If I have to find something, it's the long term psychological effects. You don't care about your former love as much as a symbol of that love, like a locket. Vampire homes are presented as formally being fancy, but have fallen into disrepair, thus matching their mental state.
But I still want to be Laszlo Cravensworth. I'm here to drink and fuck for eternity.
Many vampire myths come with some assumption that you are innately evil, from being a vessel for satan to having genuine impulses for more than just blood but cruelty and malice.
I like this take on the the vampire. To become one, you are dying, your soul moves on. A malevolent spirit then resides in your body with full access to you memories and the capability to masquerade as you in personality, but crucially, they are not the same person as they were when they were alive.
The vampire myth where you retain your soul and basically are just a superhero with stipulations basically exists for people to have the power fantasy of being one.
I think the idea is that the homeowner, the person who lives in the house, has to invite the vampire in. So just because a judge grants a vampire cop a warrant, doesn't mean he could actually enter your home if you didn't still give him permission to enter (assuming they'd actually be limited by that requirement in the first place). If vampires actually existed in real life, I think we could probably throw out most of what Bram Stoker wrote in Dracula or alot of the other folk myths.
The reason why vampires need permission to enter your house is because it is playing on the fear of the stranger. The fear that a random person who knocks on your door is a predator.
Based on that foundation, I think that the cop version would be that someone has to invite the cop. Instead of playing on the fear of the stranger, it is the fear of the unhinged police officer. If someone calls the police, then they are invited.
Answer depends more on whether or not the Vampire sparkles in the light of the UV lamp outside my apartment door.
Pretty easy to detect that with even crap tier webcams, they'll oversaturate glitch or white out.
Then its just a matter of some OpenCV code noticing the sparkles, then dumping the hidden container of holy water on the ceiling on them, and answering the door with a shotgun loaded with an oaken slug.
Next call up John Constantine and see if he knows any rival vampires that have some kind death mark on this particular vampire, or if any of them need a blood meal.
Now you probably have cred with some other vampires so further visits from further vampire cops will at the very least be even more interesting.
I just saw a video that touched on this. YouTuber Steve Lehto, a lawyer in Michigan. I think the case came maybe from Wisconsin but a judge ruled that cops could enter and search a home based on nonverbal gestures. If you want to know more check it out since I don't think I can give all the details correctly from memory. What's funny is I saw things about treating cops like vampires in the comments. They really should need an explicit invitation (or a warrant) to come in.