It took weeks, but both times, the tips grew back perfectly round and smooth, even the fingerprints are back. The regrown tips felt a bit numb for 1-2 months, but then everything was back to normal. The second time I asked a friend, who is a medical doctor, how the body "knew" the form of the fingertip and the fingerprints. Where was this information stored? His answer was basically: we have no idea, just be grateful it works.
[0] https://www.hochland-kaffee.de/media/catalog/product/cache/1...