It goes back to the French revolution where the people who sat on the left of the parliament opposed the ruling class, in that case the feudal aristocracy, while the people who supported the ruling class sat on the right of the parliament. Even after the aristocracy was gone, people started to use the term left to refer to people who oppose the ruling class of capitalist society (wealthy capital oligarchs) where as the right is those who support them.

“this isn’t right vs left, this is right vs left”

uh… okay?

Choosing between parties is arguably less democratic because in many countries with such a system, like the USA, you basically just have corporations/corporate media choosing the candidates, so your “choice” is between corporate candidates, so corporations always win. There is no option to reject the nominee entirely, while in China’s system you can reject the nominee. you can just straight up veto candidates.

Westerners often also look at the very end of the process and ignore everything leading up to it. They will say “there’s only one candidate on the ballot!” as proof it’s undemocratic (even though this happens all the time in the US too…). But this ignores the entire democratic process leading up to how the candidate gets on the ballot in the first place. In Cuba for example, candidates getting on the ballot is a two-year long process resulting from local elections and meetings with mass organizations, but they ignore this entire process and just focus on the final election at the very end.

Even though China gave up on most communist ambitions post-Dheng

No they haven’t.