In addition to the excellent explanations already here, this could also be an example of implied zeugma or syllepsis.
Syllepsis and zeugma are related terms which Wikipedia defines as "in which one single phrase or word joins different parts of a sentence". This term is especially appropriate when the different parts of the sentence use the word in different senses or meanings. A common example is the phrase "He took his hat and his leave", in which the speaker combines the literal action of take his hat (pick up his hat) and the phrase take his leave (depart). Zeugma is also featured in the comedic song "Have Some Madiera, M'Dear", which has the line "she made no reply, up her mind, and a dash for the door": She made no reply (she was silent), she made up her mind (she decided), and she made a dash for the door (she ran toward the door). By listing these unrelated actions in parallel as if they are in the same category (things she made), the sentence is deliberately complex and misleading, even to a native speaker. In this sense it is wordplay, like a pun or joke.
In your excerpt, McGonagall compares something happening literally (owls are flying) and something happening figuratively or metaphorically (rumors are flying), and comparing them directly ("A is nothing next to B", meaning that A is insignificant compared to B) even though they cannot be compared. We can understand the speaker to mean that the rumors are even more noticeable than the owls, but also that this line is stylized or humorous (which matches the rest of the Harry Potter series).