Earlier quoted context omitted.
I think our comments and discussions just add to the general confusion though, this is why I just plainly recommend SHA-3. Now if I would personally work on a project I would think of SHAKE first, and I would seriously consider KangarooTwelve (especially for tree hashing, which makes K12 better than any other hash to hash big files).
You keep saying that here, and on Twitter, and people --- not just me --- keep telling you that if you're going to recommend a hash specifically to avoid length extension attacks, 512/256 accomplishes that without requiring the adoption of new hashing code. I really don't understand the argument that people can safely type "SHA-3" but not "SHA-2 512/256". Would it help if we renamed SHA-2 512/256? We could call it SH…
Also, just looking at a reasonably recent version of Python 3.6: (dir(hashlib))
"'blake2b', 'blake2s', 'md5', 'new', 'pbkdf2_hmac', 'sha1', 'sha224', 'sha256', 'sha384', 'sha3_224', 'sha3_256', 'sha3_384', 'sha3_512', 'sha512', 'shake_128', 'shake_256']"
So - no reference to sha2_512/256 as a unique algorithm there either. Nothing in https://docs.python.org/3/library/hashlib.html either. So, the whole SHA-2 512/256 thing isn't that straightforward.
With that said, I would hope that anyone who was doing this for a real purpose would at least take 10 minutes to read the wikipedia page. And lots of useful information on crypto.stackexchange.com as well.