It's all complicated.
Iran is the remnant of the Persian Empire, and Turkey is the remnant of its ancient rival, the Ottoman Empire. Much of the northern Middle East (along with a decent chunk of Europe) was part of the Ottoman Empire until ~1900. And countries there were largely fictions of European conquest and ~colonization.
As I understand it, the Persian vs Ottoman conflict survives more or less as Shia vs Sunni. But all of them hate intervention by outsiders.
There's aren't that many Shia in UAE and Saudi Arabia, and I doubt that Iran plans their conquest. However, Iran does work with groups throughout the Middle East who are fighting against outside intervention. Even Sunni groups. But not, I gather, ISIS.
Anyway, this seems a decent overview:
https://thehill.com/opinion/international/472657-beyond-the-...
Israel
US-USSR