What coastal creature leaves braid-like trace that has clear landing and take off points?

I too think it's from a burrowing animal. Instead of crab I would say it is some kind of lugworm/sandworm.

I found this similar image:

https://www.plainpicture.com/de/images/1443397

The keywords for this image contain "Wattwurm" = lugworm, though the image might be mislabeled.

This is almost exactly the opposite of what you think it is - it is actually from a burrowing animal, so instead of flying, it is actually burrowing into the sub-surface liquifaction layer of the sand and leaving behind this imprint.

I think (correct me if I am wrong), but it is likely that the start of the burrow is the depression above your toe and the mound is above where it is hiding. If you look closely at the mound you will see a flat surface that is probably an egress point and possibly breathing hole too. If you come across a similar structure in the future, you can dig down below the mound rapidly and come across the animal that built it.

I don't know exactly which animal made this burrow, but I would guess from the form that it is a crab, certainly some form of invertebrate.

I had a fairly extensive search, but couldn't find any sea-shore guides for NY state that cover animal tracks unfortunately.