SHA256 and other hash functions, are NP-Complete problems: their solutions consume negligible time and resource to be verified, it is basic in "computer science"

Hash functions are not decision problems, so they cannot be NP-complete.
I could create a decision problem out of a hash function though.
Something relevant for mining would look like:
The set of of pairs (p,y) where
p is a bitstring of length between 0 and 256,
y is a 256 bit number,
and there exists an 256-bit x with prefix p such that SHA256(x) < y
Such a problem is in NP.
But it would still not be NP-complete, since there is no way to reduce other NP problems to this one.
Yes, my mistake to call it NP-complete, it is NP. In the context of this discussion, when we refer to hash functions, the PoW problem (like one you have suggested, a conditional hash generating problem) is what we usually mean, yet I should have been more precise.
This was posted in a chaotic atmosphere but the point is maintainable that, verifying shares (not the Prepared block or its counterpart in traditional PoW, block) is a trivial job, by definition. Because it needs just verifying an answer for a NP problem.