None of the vaccines work particularly well to stop asymptomatic spread of Omicron, even with three doses. But all vaccines, Chinese or otherwise,
appear to still be effective in preventing most severe illness, hospitalization and death. The notion China's vaccines are worse than the rest or totally ineffective was never true (78 percent efficacy was not THAT big a drop from 90-92, despite what US newspapers wanted us to think) but it's especially laughable now that Omicron has put everybody on a level playing field.
As far as Omicron spelling doom for zero-Covid, there have already been several local Omicron outbreaks, most notably in Tianjin, that were brought under control. Qingdao and Dongguan are seeing big swings right now, but they're also testing everyone. If case counts start moving into the 4 or 5 digits, that would be the time to declare zero-Covid dead.
I think people are projecting a lot of their previously held opinions on China onto its epidemic control policy and ignoring some important facts.