I'd say the US is a far more eager participant than you assume. As Biden himself has said in the past- "if Israel didn't exist, the US would have to invent one to protect US interests."

Israel is the physical embodiment of US influence in the MENA region, a key to destabilizing and controlling much of the world's oil and the trade between Europe, Asia, and east Africa. Many Israelis with dual citizenship are part of the highest levels of US administration- Yellen and Blinken being the most high-profile names that come to mind. And even now as we speak, Hochstein, Biden's energy security advisor, is in Israel talking about stealing ("developing") the offshore gas recently discovered.

I would say that it is anything but a "unfortunate coincidence" that the US is backing this genocide. It's not a one-off event, the US has backed every settler-colonial state and fascist dictatorship since WW2, and has an extensive history of instigating or otherwise supporting their acts of genocide, as well.

The situation is a disaster for the US, but as you said- they have no political path domestically to stop the genocide train, because said paths are wholly unfeasible and counterproductive to their end goals- the permanent destabilization and fragmentation of the Arab world (and the world outside the US and its western puppets, at large). Genocide is an inevitable part of the process of American hegemony to further this means, to maintain its ever-growing proxies' foothold (whether it be the encroachment of NATO, the expansion of Israel, the spread of US foreign bases, the militarization of Taiwan, it's all just part of that same pattern of never-ending expansion and aggression), and to find new reasons to terrorize the world on Wall Street's behalf again and again.

Do average Americans hate what's going on? Sure (at least, many do). And there's increasing dissent among the pencil-pushers in government as well. But none of that matters to the US, at the end of the day, because the real powers-that-be behind the US- its wealthy elites- love Israel, and they stand with white, western supremacy, and I would even go so far as to say that they love genocide, just as they love war and destruction, because it is how they came to power and how they maintain their power.