> Schmetterling may be semantically linked to butterfly via 'batter-fly' (beater-fly)
No, it's semantically linked via 'butter'. Schmetterling comes from Schmetten or Schmand which is a sort of heavy cream. There used to be a folk believe that butterflies would consume milk or butter if left uncovered. They were also sometimes called Milkdieb or milk-thief in German.
That is disputed. Most scholars say that germanic "schmand" has different roots and is cognate with English "smooth" - some scholars however consider schmand a very old loan word from proto-slavic smetana.
You would expect closely related languages to have similar words for a common animal, i.e. to be at least somewhat conserved. I do find it mysterious. Another one: Dutch vlinder, Afrikaans (very close descendant) schoenlapper.
I think the papillon dog breed has big, butterfly-like ears!
But the main reason closely related languages tend to have similar words is because the word existed before the languages diverged. When the already distinct languages borrow a word independently, the word might have a different story or source behind it.
Schmetterling may be semantically linked to butterfly via 'batter-fly' (beater-fly)
also:
motyl~moth sommerfugl~summer-fly
interesting that wiktionary for papillon shows a puppy :) might also be linked to big pupils and fake eyes
[0] https://en.wiktionary.org/wiki/papillon