i've misread the description in the RFC; we should copy up to, but not including, the next '/' at the end and manually inject some '/' in some other cases.

path should *start* with "/" to enter that branch, not be exactly "/".

make sure path starts with "/" only when there's an authority part, not when it's not there!

need to copy until the *next* path segment, otherwise we loop indefinitely if *p == '/'.

While here also add some error checking.