I don’t speak any Danish, so correct me if I’m wrong, but maybe the situation with islands is parallel to English. “I’m on Manhattan” and “I’m in Manhattan” bo

I don’t speak any Danish, so correct me if I’m wrong, but maybe the situation with islands is parallel to English. “I’m on Manhattan” and “I’m in Manhattan” both sound like fine English to me, the former having the connotation that you are specifically referring to the physical island rather than the political subdivision (borough of NYC) that roughly corresponds to it. But nobody would ever say “I’m on Jamaica” unless they were trying to advocate for some extremist political view that it’s not actually an independent country.