The documentation for the built-in function next (which calls the __next__ method on an iterator) discusses its behavior when the iterator is exhausted.
It talks about the StopIteration exception.  However, it does not say anything about calling next with two arguments.  See the library documentation at https://docs.python.org/3/library/stdtypes.html#iterator-types

My impression was that the presence of the second argument would suppress the StopIteration exception; instead next would return the value of the second argument.  That is the way that list iterators behave, for example.  This behavior should be documented.

It's documented here: https://docs.python.org/3/library/functions.html#next

The next() function has a different signature than the __next__() method.  The former takes one or two arguments.  That latter only takes one.

    >>> it = iter('abcde')
    >>> next(it)
    'a'
    >>> next(it, 'default')
    'b'
    >>> it.__next__()
    'c'
    >>> it.__next__('default')
    Traceback (most recent call last):
      File "<pyshell#4>", line 1, in <module>
        it.__next__('default')
    TypeError: expected 0 arguments, got 1