Short answer;
You are mixing the compression function and the hash function. Both pages/libraries are true on their context!
Extended answer
SHA-256 like the other hash algorithms is always padded and it is defined in NIST.FIPS.180-4
Suppose the length of the message $M$, in bits, $\ell$ is bits. Append the bit 1 to the end of the message, followed by k zero bits, where k is the smallest non-negative solution to the equation
$$\ell +1 + k \equiv 448 \bmod 512$$ Then append the 64-bit block that is equal to the number $\ell$ expressed using a binary representation
So 512 zeros bits in SHA-256 will have 447 zeros ($k$ part);
$$\text{Padded_Message} =\underbrace{\texttt{000...00}}_{512-zeros}||\texttt{1}||\underbrace{\texttt{000...00}}_{447-zeros}||\underbrace{\texttt{leng encoding}}_{64-bit}$$
If you really want to test some inputs, make sure that they are correct on the NIST's test vectors defined in Cryptographic Algorithm Validation Program - Hash functions
For padding, as usual, is not related to the user. The libraries handle the padding for the users.
Since it's exactly 512 bits, there is no splitting and no padding. But from online calculators or golang code, I would obtain the sha-256 hash of the null input to be:
As mentioned above, padding is always defined. It is part of the SHA-256 hash algorithm.
Your input is not null input, it is 512-bit zero input. NIST provides the length zero test vector and it's result as
Len = 0
Msg = 00
MD = e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855
Testing your input on sha256algorithm.com produces
f5a5fd42d16a20302798ef6ed309979b43003d2320d9f0e8ea9831a92759fb4b
I've tested this page on some NIST test vector's too.
The link you provides as SCALA MAMBA mentions as;
Output: Chaining values after compressing input block (in the same format as the digest would be returned)
IMPORTANT: These are NOT test vectors for the complete SHA-256 hash function, as the padding rules are ignored
This is the output of the first compression function. This can be verified on the sha256algorithm.com if you stop on the 164th step. Put your mouse on the initial values and you will get the hex value;
da5698be17b...
This is the same on the other link to; given as sha256 compression test vectors.
Remember the output of the compression function is the initial value of the next compression function if needed. If not needed, then it is the output of the SHA-256. The first initial values are given;
These words represent the first thirty-two bits of the fractional parts of the cube roots of the first sixty-four prime numbers
as a nothing-up-im-my-sleeve-number though this is psychological.
