I evaluated various sorts for strings as part of my winning submission to https://easyperf.net/blog/2022/05/28/Performance-analysis-an... and found https://github.com/bingmann/parallel-string-sorting to be helpful. For a single core, the fastest implementation among those in parallel-string-sorting was a radix sort, so my submission included a radix sort based on that one.

The only other contender was multi-key quicksort, which is notably not a comparison sort (i.e. a general-purpose string comparison function is not used as a subroutine of multi-key quicksort). In either case, you end up operating on something like an array of structs containing a pointer to the string, an integer offset into the string, and a few cached bytes from the string, and in either case I don't really know what problems you expect to have if you're dealing with null-terminated strings.

A very similar similar radix sort is included in https://github.com/alichraghi/zort which includes some benchmarks, but I haven't done the work to have it work on strings or arbitrary structs.