In what sense was Socrates' mission political?
If we look at Plato's dialogues, it is clear that Socrates desired to make a political impact among the Athenians.
For example, Socrates states that his mission was to be a gadfly to cause the Athenians to seek truth. He considered the Athenians to be a dim-witted horse that needed to be goaded in the right direction. This is why he believed that the Athenian government should reward him instead of punishing him.
"If you kill a man like me, you will injure yourselves more than you will injure me," because his role was that of a gadfly, "to sting people and whip them into a fury, all in the service of truth."
For another example, all you need to do is to consider the Republic. The whole work is about the ideal polis, which is political.