The other diplomatic offices are consulates.
If it's anything like the Chinese Embassy in New Zealand, there's usually regular protests outside, for a variety of reasons. Their response would be to ignore them, like they usually do.
I spent two years in Hong Kong. There were frequent (weekly) protests at Chinese buildings (I remember one in particular that seemed to always have a crowd of people, in Sheung Wan, on Connaught Road I think?). It was always super peaceful, from both sides.
The Beijing liaison office. That's attracted a lot of protests in the past few weeks, and has had a temporary barricade around it for about as long.
HK is doomed for sure, but Taiwan isn't.
I'd be a little surprised if there haven't been similar at embassies in the US - perhaps they're just not attracting enough numbers to be widely reported?