Does this imply the CPC must be a democratic organization?
CPC practices democratic centralism, but why does it even matter? CPC members still have to win their election to actually become a member of the government, and it's an election everyone has the right to vote in, not just CPC members. Technically, you don't even need to be a CPC member to run for office, there are independents and members of other parties in China's government, even in the National People's Congress. If they had no connection to the people then they would not be voted into office.
In most provinces, direct voting by the masses exists only at the local level
Nation-wide direct voting doesn't work for a big country, it's literally physically impossible and always produces oligarchy/autocracy in practice.
Take something like the US national presidential election, most Americans can only name like 2 candidates who run for their national presidential election, and in rare instances 3-4, despite often hundreds running. Why? It's not physically possible to come to organically know candidates on a national level, if Biden personally talked to every eligible voter for 1 minute it would take over 300 years. That means the only way people can actually learn about candidates is through some sort of media infrastructure, they learn about people like Biden and Trump from the television.
But the problem with this system is that you obviously cannot vote for someone you don't know who they are, so the television really gets to decide who is actually electable in the first place. The candidates people are more likely to know about can be predicted most accurately based on how much money they raise, because that's what they use to pay for media slots, and therefore the slate of candidates you get to pick from will always ultimately be decided by the television and it is physically impossible for it to be any other way.
Of course, in capitalist countries, the media is privately controlled, and so money comes from private enterprise, and so the slate of candidates is always pro-capitalist. But you can't solve this problem just by nationalizing media because then you'd end up handing over who picks the slate of candidates to a shadow government deep state esque clique.
A much better system is a system which always tries to keep elections small-scale. You have local elections in your local area that elect a representative to a higher body, such as a county's government, and then each of the representatives in the county government elects a representative to the provincial government, and then all the representatives of the provincial government elect candidates to the national government, and then the national government elects the president.
At no point do you end up with a single election that involves hundreds of millions of people or the whole nation simultaneously, so it is always something an individual can grasp what is going on organically, so it more accurately can capture the desires of the actual population and not just the whims of whatever happens to be on television at the time.
only between candidates pre-approved by the CPC
You need CPC approval to join the CPC, you don't have to join the CPC to run for the government. And the CPC is not a party like in western countries where you just join and do nothing but show up to vote every few years. If you join the CPC you are expected to do real work, they send CPC members out to help during natural disaster relief, they send out CPC members to help with poverty alleviation drives, you sometimes see signs up with phone numbers of your local CPC member to call if you need assistance with anything. They are expected to be actually be active community organizations that help out the public and so obviously you need an approval process for the CPC, it wouldn't function without it.
What power does the proletariat itself hold over the party’s rule? If the proletariat truly does not approve of their representation, do they have the power to reject it?
Yes. Don't vote for them. In fact, you have more democratic choice in China than in liberal democracies.
Imagine if you had a system where the CPC really did just pre-pick every candidate and then you had "competitive" elections between their pre-chosen candidates. Would that be democracy? Of course not, but why? Because the same institution picked all the candidates so no matter what the institution wins. That's how liberal democracy works: the corporate media ultimately nominates all the candidates and so no matter what private corporations always win. There is no "out."
In China candidates have to get 50%+1 of the votes to win so you can just straight-up reject the nominee.
There is a white paper here that talks in more detail about the whole topic of what people can do to hold the government and party accountable in general.