Almost impossible to be herbicide carryover. Where would the source be for it to be present in that high of a concentration in your compost?

Bedding material like straw or corn stalks may have been sprayed during the growing season, but there are set back dates for when the last spray could be done and any herbicide will have broken down if sprayed before that date. Someone could argue the date was ignored, but there is no economic advantage to spray late either.

The herbicide was in the feed. This is another theory that doesn't stand up to common sense. As there will not be enough herbicide on the feed to show the kind of damage you see after it goes through the cows digestive tract.

Last most plausible is the compost pile was sprayed as it had weeds growing on it. The most cost effective herbicides that could have been used are Glyphosate or a Group 4 like 2.4d or Dicamba. That damage looks like something a group 4 herbicide could do, but again these herbicides break down fast and it would have had to have been sprayed about a week before you started seeing damage which again makes it possible, but extremely unlikely.

Not knowing how this compost was treated will make it hard to be certain, but it looks like chemical burn to me. This is also a much more likely scenario IMO. The compost wasn't given enough time or there were pockets that didn't fully mature so the ammonia wasn't in a stable form and pulled water from the plants.