Actually, You should read Jon Entine’s Abraham’s Children, about Jews and DNA. You know who the closest genetic relatives are to modern day Arabs (those on the Eastern shores of the Mediterranean, at least)? Yep. Us. You and Me, and every other Jewish community whose haplotypes were included in the studies he researched and quoted.
Persians are considered part of the Indo-Iranian group of ethnicities, and they migrated from Central Asia. They are linguistically distinct (speaking farsi/persian rather than Arabic, which is a lot closer to Hebrew). The Arabs originated in the Arabian peninsula, and are a distinct ethnic, linguistic, and genetic group.
North Africans are a different story. There are a few groups. In Egypt, there was and is a large ethnic subgroup that developed along the Nile, but it had a lot of interplay with Phoenicians, Hyksos, Nubian and other African groups, so there is less ethnic and genetic cohesion. In the Libya/Tunisia area, there is the remnant of the Carthaginian pepoples, who were related to the Phoenicians and the Greeks. Further West there was a larger Berber influence, which came from the Saharan interior. But overlaying all of this was the massive influx of Arabs in the 700’s, which radically changed the demographic makeup of North Africa.
I agree that North Africans by and large describe themselves as part of the Arab Ummah. The modern Persians definitely do not.