> even if we saw it a year early, what could we do about it?

You could try sticking various forms of interceptors on it's path, at those speeds it's probably not maneuvering so relatively easy to intercept if you have warning.

I'm not sure to what degree we could deflect it or mitigate the damage, but I wouldn't be surprised if it was a sizeable one. Any collision is going to convert a ton of energy from kinetic energy to thermal energy, which should in large part radiate away before impacting earth. We could also do various clever things like putting hydrogen targets in the way which would undergo fusion upon collision with an object moving at relativistic speeds.

My thinking is that if you have a rock headed your way at say 10% of lightspeed or so, pretty much anything you can do to it past a certain point is mostly just going to change what form of matter smacks into your planet.

Maybe my mental model for how that works is wrong, but I'm just picturing a dust/rubble cloud at 10% of c irradiating the planet with xrays or something due to whatever extreme friction interaction happens in the atmosphere.