Here's the thing though, those people can buy tires or pants made in China, WITHOUT using Chinese websites.
I seriously don't think they care if we use Baidu or not. In fact, I wouldn't be surprised if the party would PREFER that we NOT use Baidu.
Not to mention the enhancement in global surveillance it would give the CCP.
If the world used Baidu, it would be a propaganda coup for the CCP. They'd have the ability to disappear information they want to suppress (like criticism of the camps in Xinjiang), and freely push propaganda and disinformation (a la https://en.wikipedia.org/wiki/Operation_Infektion).
Think about it: if the web existing in the 1980s and the Soviets controlled the world's main search engine, the top results for "AIDS" would be disinformation articles about how the US government created it.
So, I'm sure the CCP would like the world to use Baidu, but it might not be high on their list of priorities to push right now.
Soviets tended to play up the bad points in their propaganda, so it would likely be pushing images and videos of people suffering with AIDS, captioned with "American pigs aren't researching or treating this mass epidemic ripping through their capitalist stronghold".
The sad part is such propaganda would be fairly accurate, for most of the 1970s and 1980s our government stood by and let people die of AIDS, not funding research or pushing safe sex education, feeding the epidemic.
Soviets tended to play up the bad points in their propaganda, so it would likely be pushing images and videos of people suffering with AIDS, captioned with "American pigs aren't researching or treating this mass epidemic ripping through their capitalist stronghold".