Most of these surgeries use insensate flaps so usually don’t connect nerves, but there are ones that do connect the nerves. Nerve regeneration is just much more finicky than arteries and veins so it’s usually not worth it.

ENT here. They mention it towards the end of the article, but they end up transplanting the nose in what’s called a “free flap surgery”. It’s a common procedure in head and neck surgery for reconstruction after cancer removal. It involves taking skin, soft tissue, bone, muscle (with its associated arteries and veins) from places like your forearm, thigh, leg, scapula, etc. and transplanting them to other places where you hook up donor and recipient veins and arteries using microsurgery. I work on ~4-5 of these cases a week where we have patients with tongue, throat, etc. cancer where we replace missing tissue after cancer removal with donor tissue from elsewhere in the body.