All I can say is I feel your pain. My family owned and operated chicken houses for decades. The property being in the family for over 100yrs. Some development company bought land next door and built a subdivision. They built right up to the property line. Many times the builders were caught trespassing and trying to use their land for access and to dump dirt and debris during the building phase. Anyways, people moved in, they got a property line inspector to come out and removed 1ft from the property line all the way around for a total of 1 acre removed. The neighbor then placed a solid 15 foot long wood fence within 9ft of one end of the chicken house. Then they called the building inspector who told them they could no longer operate that chicken house because the fence had to be at least 10ft away. It became a financial burden. That fence was obviously placed there intentionally for that purpose. If they didn't like chicken houses they should not have moved there. Some people have zero consideration for others, think they themselves are on a level above others or something sick like that.
We still kept pet chickens and pea fowl (who can be quite noisy lol). I caught the neighbors kids an older brother and younger sister in the act of breaking into that chicken house and letting their labrador mix dog chase and kill our birds. I caught them because I came home from school and heard them cheering the dog on. I chased them off with a shotgun. I was probably about 10y/o at the time, about the time when I realized what evil truly was. When their parents were confronted with my parents and the police they of course denied it.
Look into spite laws and lawyers, don't let this neighbor walk all over you.

And keep a watchful eye on your birds, maybe place a camera on them if you haven't already.