I don't have any inside knowledge unfortunately. The clip I watched was someone shouting about covid policy, but it may not be the theme for others. Foxconn workers happened a few days ago was mainly about compensation, of course covid policy can be one factor, but it was not correctly portrayed in media.
I accidentally watched a clip on Chinese TikTok, this multi-city protests were announced vaguely by some random guy, so I believe this is at least organized. I would think there are supporters in government. My understanding is that politicians are always politicians, people may be protest something, politicians can support/oppose it for totally different reasons. So yes and no. I sense there is a lot going on. The government is now at a very awkward position.