exchanged "^~" with "~" as a pattern matching in the location part.
I am very sure, that it only works using "~". I am not quite sure though, if this is the right way to do it, because "~" is probably more expensive than "^~"

the rewrite has to be behind the definition of the $backend. Otherwise nginx will fail to work. This is probably because "break" goes directly to the proxy_pass which uses $backend.