Should the West capitalise on China's protest problems?

Whenever any sort of uprising occurs in a country which is not allied to or friendly with the United States the government of that country will often acuse the Americans and the West of being behind the demostrations, stirring it up for ideological and hostile reasons. Tehran always tries to blame the US for anything going wrong in Iran. Like now for example, with young women and others protesting across the country over the killing of a woman in prison who had refused to wear the hijab in public. I sincerely doubt the CIA or any other US organisation is playing any role in the demonstrations. The young people of Iran have enough fire in their bellies to protest by themselves without any foreign backing. The same can be said about the spreading protests in China over President Xi Zinping's zero-Covid policy and the nationwide lockdowns that have shut Chinese people inside their homes for weeks. The angry Chinese demonstrators are brave enough to carry out the protests and demand Xi's resignation and the end of communist rule and don't need or want outside help. But with China facing demonstrations on a scale not seen since Tiananman Square in 1989, should the Biden administration make a conscious effort to highlight the repression that's going on in China and try to exploit the challenges now facing the Chinese president-for-life? It's a tricky one. Diplomatic relations between Washington and Beijing are fragile at best and an overt policy of backing the protesters would hardly improve matters. In my view, Biden should refrain from gloating publicly about Beijing's problems but focus any criticism on the harsh methods being used by the Chinese security authorities to clamp down on the demonstrators. We saw how protesters were attacked and abused during the riots in Hong Kong in 2019 and 2020. This sort of over-the-top police suppression needs to be highlighted. It will anger Xi no doubt but he is facing humiliation at the hands of the thousands of protesters and he needs to be held to account on the world stage.