Publishing a paper can be an imperfect, but useful 'expensive signal' that increases visibility. For vqsort, we initiated a collaboration with two universities who had published papers: KIT's ips4o for parallel sorting; Jena's fast AVX2 partition and 2D sorting network.
It needn't be AVX-512, but I'd consider AVX2 to be table stakes for any sorting algorithm. It's not clear that scalar techniques transfer to vector approaches (for example, multi-pivot partitioning did not help), and the speedup from AVX2 vs scalar is at least 3x.
It's not clear to me that special-casing already-sorted inputs is a net positive in practice outside of benchmarks. Sure, we can early-out as soon as a difference is found, but we're still paying for potentially an entire scan through the array, or a slowdown in partitioning (we found that even tracking the min/max had a noticeable cost). This can instead be done at the level of callers, who can then remember that this dataset is sorted and even skip the is-sorted check subsequently.
In-place seems helpful for benefiting from limited-size but faster memory such as L3 or even HBM.
Finally, why C? As you mention, AVX-512 is not ubiquitous, and we'd prefer portability over duplicating several thousand LOC for each instruction set. That's much easier (via Highway) in C++. Would a C-compatible FFI be enough?