China should assume that William Burns was not bluffing. As long as there is a US Embassy and Consulates on Chinese soil, the CIA is guaranteed to be there. If the CIA is confident about rebuilding its spy networks in China, there is no harm for China to carry out another espionage audit. Who knows what could be uncovered.
Few years ago there was this person Chuang Tsu-i, supposedly a Taiwan-born US citizen. She was in Chengdu as wife of the US consul general whatsisname, mostly playing the part of 'friendly overseas Chinese happily back in China' but occasionally getting into spats with locals over her boba lib opinions.
Things got curious when China ordered the closure of the US consulate in Chengdu. Chuang was not listed on the official consulate roster as the spouse of the consul general. Later, back in the US, she was apparently homeless with her children, while her husband whatsisname was already posted to another US diplomatic mission elsewhere. There was speculation that she was from Taiwan's intel service.
Here's Sima Nan talking about her.