My neighbours were finally here. They're starting to work on it
today. They're emptying out their courtyard to make space for the parts of their barn they're gonna tear down. Also organizing a mobile elevating work platform (big ass machinery) and calling our mayor for a permit.
They'll tear down the attic and upper level of their barn, leaving the lower walls standing. At least that's the plan. Whatever will fall while they're working will fall. I hope my witchhouse will survive this, but since part of the wall already fell on it.... who knows. If there's more coming down, it may be crushed under the barn walls. They couldn't promise me.
But as long as my main house stays intact, we'll find a solution. They're starting from the front, which is more stable and in parts next to my main house (less than a yard between them; if I reach out to the left of my bathroom window, I can touch the roof of their barn).
I already hear them working in their yard.