Why do they need to effectively wipe them out? I'm just not clear on why that apparently NEEDS to happen. It's not necessary to do all that to illustrate the power of the race, it just generally feels like overkill.

If you want to establish them as being an elite fighting force when they DO go into combat, then go the route of the attempted assassination (likely a successful assassination if it was going to spark so much violence) triggering an space version of a world war. Factions on both sides, and the Yuan-ti, though perhaps not as large in number as some of the other races, generally hit like a scalpel in whatever battles they took part in- they would go in and with surgical precision eliminate their targets, take the strategic locations, and with the finesse of a surgeon carving out a tumor, they would neatly slice out any trace of opposing military activity.

Another thing to recall is that it's almost never the people who want war, it's the ones in power- and they need to get the propaganda machines up and running to make the people have any desire to go out and kill. Knowing that, if the Yuan-ti went after their enemy's ability to disseminate propaganda, they could cause them to lose the support of their population, meaning no new soldiers joining by choice, and a soldier that's been drafted won't fight as well. Effectively, turning their own population against them.

There's no need to destroy that which you can turn to your advantage. Wiping out a civilization is a needless use of energy when you can use one half of that civilization to help wipe out the half that's actually causing problems.