All good - this was my mistake.
I imported first and created the custom fields afterwards. For whatever reason I was expecting that MC supports the ID3v2 tags without the need to create these fields in advance. Then I realized these fields are not there by deafult. After creating these fields I expected some magic to happen automatically.
In fact, instead of waiting for magic I had to perform 'Update Library (from tags)' from Library Tools. After that 'Artist Sort' gets updated.
So hopefully, when I create all the fields that I want to use (and show up in Tag Dump) they will will appear in Advanced after Update Library. If not, I will let you know.
Thanks for your support and patience and for your quick replies!