How can I close-read the passage that begins, "'Our Leader, Comrade Napoleon', announced Squealer, speaking very slowly . . . " and ends " . . . squealing with pain and terror, to Napoleon's feet," and analyze how this passage highlights the themes of propaganda and the abuse of power?

Propaganda is information that is not based on objective truth, but is biased or dishonest. It is meant solely to promote the ideas or ideology of one group or political party.
We can see in this passage how the pigs use propaganda to promote Napoleon and make the false claim that Snowball is a traitor. Squealer delivers the propaganda as if it is truth, and uses as his authority Snowball's enemy Napoleon. In actuality, however, there is not one shred of evidence that Snowball was in league with Farmer Jones or was his agent from before the time of the Rebellion. It places all its credibility in the idea that whatever Napoleon declares must be true—and we see Boxer fall for this ploy. Further, as far as diction goes, Squealer repeats the word "categorically" twice. We already know that most of the animals don't understand words of more than one or two syllables, so it is very unlikely they will know what this word means. However, like most propaganda, though empty of any real content, it sounds impressive and important, so the animals are more likely to believe in Snowball's guilt.
Then, when Boxer backs up Squealer's claims, Squealer uses emphatic diction (emphasized with an exclamation point) to praise Boxer and also calls him "comrade," perpetrating the fiction that all the animals are equal. Napoleon awarding himself medals of honor as a "hero" is also a piece of propaganda. Napoleon has never done anything remotely heroic, but propaganda replaces truth with lies.
As for abuse of power, that occurs when governments stop following the rule of law and do exactly what they want because they can. We see this at the end of the passage. Without any due process or accusation of wrongdoing, Napoleon simply has his guard dogs (representing sheer brute force) leap forward and drag four pigs to the platform. The text tells us the four pigs are terrified and in pain. Napoleon has pulled off a power play, in which simply dragging the pigs forward spreads terror and implies that they are guilty of some undefined crime. In a state that respected people's rights, this would never happen.