You might want to check your sources. Jefferson and Hamilton, but primarily Jefferson, started the partisanship during Washington's administration. Jefferson was always messing around in the background trying to get the US to take the side of the French radicals against the British and even had surrogates trashing Washington in an attempt to force him to change his stance on neutrality.
Adams, like Washington, had little use for partisan politics. As president, Adams managed to piss off both sides because he would not give into to either of their demands.
Adams did not have the temperament to be a politician. He was far too blunt and stubborn to play political games.
You're right: Adams didn't try to load the courts with Federalist judges up until the eve of Jefferson's inauguration; there were no such thing as Midnight Judges. I guess the facts that brought about Marbury v. Madison were complete fiction.
No political games there!
Factionalism is not bad. You do not get a pearl, save for friction.
BTW, to confirm your view of Adams, he left Washington before TJ's inauguration, not out of disgust, but relief to finally be out. It brings to mind Washington's comment to him as he stepped down, "I am rightly out, and you are rightly in. Let's see which of us is the happiest."