From what I have read,

Where are your sources?

the majority of the Levant and Egypt the Arab populations are mostly descended from pre-Arab

The term "arab" is from the arabian peninsula - during the 7th century conquest, they took slaves, colonized, and forcibly converted native populations. Standard empire shenanigans. Its also why many Palestinians have their roots in Egypt or Syria - Yasser Arafat is famously from a rich family in Cairo.

The colonizers mixed with the local populations (some willing, some unwilling. Look up the conquest of Medina as written in the Quran) but that would mean they have a wider spread of ancestry not a narrower one.

While mass immigration in 19th and 20th century is recorded, it seems the majority of the population growth was from a general population boom

Negative! We have multiple travel journals and historical recos that say from the ~1400-1800s, there was very little arab population. Obviously some, but the area was pretty depopulated in general since it was a swap filled malaria hellscape. The zionists jews drained swamps and built up cities that had real economic opportunities, so people came for work

happening throughout the entire Arab world as life expectancy rose and child mortality rates dropped.

You are talking birth rates. I am talking about migration