Home nation status is the same as England, Wales, Scotland and Northern Ireland. As of now, Cornwall is considered no different from the rest of England. But when most people there say "England" they really mean England outside of Cornwall, they used to have their own language, they are mostly ethnically Celtic. It's quite similar to Wales in most ways. So I would support home nation status for Cornwall.
This is probably blasphemy in some circles but even the Irish are not mostly ethnically celtic. DNA evidence suggests that the Irish and other British peoples for that matter are mostly descended from the paleolithic hunters gatherers who originally settled in the Isles. The celts were basically a cultural overlay on the Irish population like the Normans in England and Ireland. The most lasting "Celtic" element in Ireland is the Irish language which was the language of the Celtic invaders and eventually was adopted by the general populace. The fetishing of all things Celtic occured in the 19th century abetted by the Romantic era and the quest to delineate themselves from the English overlords.