what do shluchim do in Russia or Muslim countries or in EY?
Shluchim in Russia do Julian, if I’m not mistaken.
EY does Gregorian.
Muslim countries: Not sure what their minhag is l’poel.
From here it’s implied that they don’t do nittel at all:
https://hebrewbooks.org/pdfpager.aspx?req=4615&st=&pgnum=360