We’ve now confirmed that Tesla has started shipping cars with the new headlights for the Model Y in the US. Reddit user /u/kaess posted on Feb 6, 2021 photos of their Model Y Performance. According to their post, the car build date is 2/5/21 with VIN 124,xxx making it one of the highest VINs being delivered at this point.
The new headlights have xenon projector housing which allows for more defined headlights and cutover over the existing ones.
Here is a side by side picture. The top is the old headlight (from a Model 3) and the bottom is the new headlight. You can see the projector on the new headlight.