Are the people living there angry?

Yes, I think they're seething with anger.

Not sure where the street comes into it, though. Are they holding a public protest?

#3: In such a case native speakers of English would most probably use the plural: the seething Syrian streets. Is the author likely to be a native speaker?

Zum zeitgeschichtlichen Kontext, aus dem Wiki-Link in #4 :

 The Tadamon massacre[1] was a massacre that took place in the Tadamon neighbourhood of the Syrian capital of Damascus[2], Damascus, on the 16 April 2013 during the Syrian civil war. Soldiers affiliated with the Syrian Armed Forces, specifically Branch 227 of the Military Intelligence Division[3], killed more than 280 civilians who were taken to one of the isolated neighborhoods of Damascus, and they were executed one after the other in a mass grave that had been prepared in advance, as stated in the extensive investigation that was initially published in the American New Lines Magazine, followed by a lengthy and comprehensive investigation published by the British newspaper The Guardian.[4][5] ...

Der Guardian-Link in #4 gehört immerhin schon mal zum Zitat im OP ...

OED

street

3. In specific uses, chiefly with the.

d. The streets regarded as the realm of ordinary people, and especially as the source of popular political support for a cause or party.

...

1969   Listener 24 Apr. 555/3  This was the street taking over a modern state in a way which hasn't happened, I think, at any other time in our history.

2005   R. Nidel World Music: Basics iii. 190  Abdel El Halim Hafez...was the golden boy of the Nationalist revolution in 1952 when pan-Arabism arose, the darling of Nasser and the street.

Here's an article about the "Arab street" and similar expressions. https://merip.org/2003/03/the-street-and-the-...

And Wikipedia: https://en.wikipedia.org/wiki/Arab_street