Wrong, virtually every source states that he was an Yemeni Arab. There were close to no Persians in Yemen ever. Especially not 500 years after the appearance of Islam! The word itself is also of Arabic origin.
Well, there are 1.5 million Arabs in Iran. Many millions more that are partially Arab. So I highly doubt that. Overall it's about the same number but most of the Persians in those countries are not nationals in particular in the UAE where there are a lot of Persians/Lurs. While the Iranian Arabs in Iran have lived in what is now Iran before the appearance of Islam and are obviously citizens and not new arrivals.
Sayyid/Ashraf means that you are an descendent of Ali ibn Abi Talib (ra) on your paternal lineage (father to son etc.) thus your lineage is Arab. Does not matter if that lineage has intermarried with non-Arabs for generations like most have anyway. Doest not change your overall paternal lineage. That's the point of surnames, lineages etc.
I know about the closeness of Bakhtiaris and Lurs with Persians and I agree with your categorization/comparison. I stated the same earlier if you have noticed.
Gilakis and Mazandarins from what I have gathered seem closer to the Caucasian peoples and seem like a hybrid between them and Persians. But I am sure that @
rmi5 knows more about this than most here.
Most of the Iraqis of Persian/Persian mixed ancestry where indeed kicked out by Saddam Hussein but there are still some left. Not a big group though. But obviously there will be mixture going on in the region between neighboring peoples, regions etc. which genetics confirm.
But as I said historically speaking the peoples of Iran that the Arabs have had most ties with where the Persians/Lurs/Bakthiaris and then Kurds. In my opinion at least. Baluch's also but that is mainly confined to Oman and is fairly recent.