C# - dateTime.ToLocalTime().ToString("MMM dd") abbreviated month doesn't works with Korean language

Question

The format MMM to the month doesn't format Jan, Fev, Mar... to Korean date.
For example:
DateTime date = new DateTime(2022, 1, 31);
date.ToLocalTime().ToString("MMM dd"); //=> "1 31"

The same problem using other way.
CultureInfo ci = CultureInfo.CreateSpecificCulture("ko-KR");
DateTimeFormatInfo dtfi = ci.DateTimeFormat;
dtfi.AbbreviatedMonthNames // => {"01","02","03","04","05","06", ...}

Answer 1

Interesting that when querying SQL-Server via

SELECT dateformat,name, alias, months FROM sys.syslanguages WHERE alias = 'Korean'

The correct results are returned. Seems a hack for C# would be to create your own class as it's unlikely AbbreviatedMonthNames is going to change any time soon.

A starter

public class Korean
{
    private static readonly CultureInfo _cultureInfo = CultureInfo.CreateSpecificCulture("ko-KR");
    private static readonly DateTimeFormatInfo _dateTimeFormatInfo = _cultureInfo.DateTimeFormat;

    public static string[] AbbreviatedMonthNames()
    {
        _dateTimeFormatInfo.AbbreviatedMonthNames = new[] 
            { "01", "02", "03", "04", "05", "06", "07", "08", "09", "10", "11", "12", "" };
        _dateTimeFormatInfo.AbbreviatedMonthGenitiveNames = _dateTimeFormatInfo.AbbreviatedMonthNames;
        return _dateTimeFormatInfo.AbbreviatedMonthGenitiveNames.Take(12).ToArray();
    }
}