I doubt the broken spoke could have caused the problem. Also I'm not 100% sure you really have a problem, though it looks likely.

Hold the bike up by seat and stem, and put your foot against the center of the right crank, and push it across to the left flexing the frame. Look to see if the crack enlarges or moves as you do so. If not, odds are it's surface damage at the junction, which can sometimes happen if the paint is more brittle than the stays.

In all honesty, I don't expect you'll be so lucky, and that there will be movement at the crack. In that case, the frame is toast, though there are some folks that repair carbon frames. It isn't cheap though, and not all frames are saveable.

There are a number of folks who specialize in carbon frame repair, so you might email the photo to a few and ask if they think they can save it, and a rough (very rough) estimate, to see if it's in your budget ballpark.