Beating quicksort alone is almost always as easy as swapping insertion sort once you get down to around 14 elements. This is used by C#'s quicksort (which also swaps to heapsort after a depth of 32 IIRC) and also in Timsort in JS, Java, Python, etc.

Blitsort is a hybrid quicksort, see title.

It is slower than it's unstable brother, aptly named crumsort. https://github.com/scandum/crumsort

Quicksort isn’t stable.

Schoolbook exchange quicksort isn't stable, but quicksort absolutely can be implemented stably, which I do in glidesort: https://www.youtube.com/watch?v=2y3IK1l6PI4.

Further to that, many use cases of Quicksort have unique keys, so stable is the same as unstable. Example: ascending indices appended to the key, when sorting large records where we don't want to move around the entire record.