There are definitely microphones that can do it. You ever seen one of those microphones that look kinda like a little satellite dish? They pick up sound from long distances. They can also sometimes pick up stuff through walls. They also make microphones that you can put up to things to listen through them. But that might not even be it. Your neighbor could have something in your apartment, . Get something high high pitched, start whispering so your neighbor turns up their listening device, then blast the high pitched sound. Like hit the test button on your smoke detector. Maybe first go from room to room whispering to see if your neighbor can hear in every room or not. That’ll help determine what they’re doing to listen, and you’ll want to blast the sound in a room they can hear it in.

You should also report them for banging on the walls. You can tell your landlord, or make a police report, or both. Get some recordings of it. Record for a week or two, then complain with the recordings. It’s harassment that prevents the peaceful enjoyment of your property. Once you put your landlord on notice about it, they have to handle your neighbor, or they are in breach of the lease. I usually wouldn’t recommend the cops unless the landlord fails, but with this situation, the neighbor is sus, and I’d worry about them retaliating, and I’d want to get he cops involved because of the potential eavesdropping/wiretapping. If you get the police on it now, then if someone happens in the near future, your neighbor will be the top suspect.