Huawei sure, no one knows who really owns/controls them. But Baidu, Alibaba, actually have fairly transparent ownership structures, they aren’t that subject to party control beyond say an American company operating a branch in China.
Working in China for 10 years, I can’t say that I didn’t feel the party at all, but their influence in our work was pretty much nil. They mostly interfered in the distribution of benefits and such.
Their policy is trickling down gradually.
They recently inserted Commissars into a list of Hong Kong real estate companies. So even non-mainland chinese companies are not immune.
Some are public. Some hide their identities (but serve similar purpose). Secret ones usually are used in dealing with foreign entities (i.e. non-mainland). So you may not even know there is one except if you are in the top management.