functools.update_wrapper inadvertently overwrites the just set __wrapped__ attribute when it updates the contents of __dict__.

This means the intended __wrapped__ chain is never created - instead, for every function in a wrapper stack, __wrapped__ will always refer to the innermost function.

This means that using __wrapped__ to bypass functools.lru_cache doesn't work correctly if the decorated function already has __wrapped__ set.

Explicitly setting __signature__ fortunately still works correctly, since that is checked before recursing down through __wrapped__ in inspect.signature.