Following up your post (thank you) I see The Jewish Virtual Library does have information about the Jews from Arab countries who migrated to Israel on another page. It relates the history of all the Jews who migrated to Israel from Arab countries starting in 1948 after they were expelled or had to leave.
They write:
Of the 820,000 Jewish refugees [from Arab countries] between 1948 and 1972, more than 200,000 found refuge in Europe and North America while 586,000 were resettled in Israel
https://www.jewishvirtuallibrary.org/jewish-refugees-from-arab-countries
So presumably some of the later (post 1972) American migrants to Israel may also have originally been from Arab countries or descended from them.
The Arab countries they list, from which the Jews who had lived there were expelled, are
Algeria, Egypt, Iraq, Libya, Morocco, Syria, Tunisia, Yemen. I had thought Iran too but don’t see that.
Not that this means Americans are a minority group in Israeli as far as I can make out, rather than the second largest group after FSU. Though I can see what you are saying that not all American Israelis live in Israel.
You may be in a far better position to know about the demographics of the present illegal Israeli settlers, but a lot of funding for the settlers is American.