Flukx
I *guess* this is a kind of unclear case: someone described the Faroe Islands as "as independent as one can get without having an UN seat". For example the members of the government are called ministers. (Correct me if I am mistaken!)
To answer the question concerning OSM: in https://wiki.openstreetmap.org/wiki/Key:admin_level links to https://wiki.openstreetmap.org/wiki/Tag:boundary%3Dadministrative#10_admin_level_values_for_specific_countries which states:
„There is some controversy about what is the exact meaning of country. For the sake of clarity, only political entities listed on the ISO 3166 standard are to be considered countries. There also exist some dependent territories and special areas of geographical interest which do have their own ISO 3166-1 code but aren't a country. [...]“ This norm is listed on Wikipedia: https://en.wikipedia.org/wiki/ISO_3166-1#Current_codes and lists the Faroe Islands.

If this answers your question, please mark this as "resolved" and maybe add a note in the Faroe OSM wiki page https://wiki.openstreetmap.org/wiki/WikiProject_Faroe_Islands so that the question will be answered in the future as well.