Carbonated?
Doogh is and is not carbonated. It depends. As sold in the streets of Iran, they are carbonated. Like Doogh of Abali. But if you step into a good classy restaurant in Iran, or anywhere else, doogh is not carbonated and is homemade.

In homes, people often make and drink the homemade uncarbonated version, unless they buy it from the grocery shop or something.

This also applies to outside Iran. Here in Texas, they sell the carbonated version in "Ali Baba's Mediterranean food store" (the biggest Iranian food store in town). But if you go to "Shiraz Persian Cuisine" restaurant, youll be served the uncarbonated version.