Are they doing that for every wrong question on every paper? That would take forever!

I work in education in Texas. Yes, they do. And yes, it does. Now, most things are digital, so they have kids make a copy of the Google Doc and then grade that and leave comments on it. But if they have paper assignments, they often leave notes on them. Leaving notes on assignments and tests/quizzes (which is likely what this was) is part of their professional review.

Also, part of their regular professional review is whether or not they're keeping proper documentation on student behavior. Different tiers of behavioral issues require different documentation/communication. So, not only are they writing notes on tests/assignments, they're writing documentation on hundreds of students, contacting dozens of parents, creating lesson plans that have to be available in advance for parental review in case any parents want to dispute the materials, and they're getting regular reviews.

And then, when all the kids are off enjoying summer, the teachers are working their summer job to supplement their shitty pay. And they're going to mandatory "Professional Learning" courses to keep their teaching certification, some of which they are required to pay from their own pocket to attend.

In San Antonio, we don't really have any "small" districts, so the numbers in the second paragraph assumes an elementary school of 300-600, middle school of 800-1200, or high school of 1200-2000 students.