With GNU ls:
ls -1 -v
ls --format=single-column --sort=version
With GNU sort (and assuming file names don't contain newline characters):
ls | sort -V
ls | sort --version-sort
With zsh, you can also get globs to sort numerically with the n glob qualifier:
print -rC1 -- *(Nn)
(here also using the Nullglob qualifier so it prints nothing instead of giving an error if there's no matching file (no non-hidden files with * as the pattern)).
If passing to ls, you'd need to tell ls to disable its own sorting (-U / --sort=none with GNU ls):
ls -ldU -- *(n)
(here, not using N because if not passed any argument, ls will list . instead of listing nothing).
You can also make it the default there with set -o numericglobsort.
But maybe better here would be to use 0-padding in your file names so they sort the same numerically and lexically:
mkdir site_{01..44} # zsh, bash, yash -o braceexpand
mkdir site_{1..44%02d} # ksh93
GNU's sort -h itself it to sort human readable sizes as displayed by du -h or ls -sh for instance where 123456789 for instance is represented as 118M, so it's of no use here.
In your case as those site_1... do not start with what looks like a human readable size, they are all considered as 0 and sort the same. You do however get a lexical sort thanks to the last-resort comparison which breaks ties by comparing full lines lexically.
Even if your directories were named site_314, site_1.1K, site_0.9M and you wanted to sort them based on the size found after the _, you'd need to tell sort where the human readable size is as in sort -t_ -k1,1 -k2h to sort first on the part before the first _ lexically, and then on the part after the _, interpreting it as a human readable size with the h flag to the key specification.
sort,-hcompares things like1Gwith100Metc. whereas what I think you want is-V. To get a list of the directories that you just created, the easiest would be to use the same brace expansion though:printf '%s\n' site_{1..44}. I'm uncertain why you feel you need to parse the output ofls, so I'm not turning this into an answer. See alsols -von a GNU system. – Kusalananda Dec 02 '21 at 14:06