Is it legal for schools to publish SAT scores to the student body...

It is a district or independent HS decision whether to put standardized test scores on the transcript. I think schools that do it started as a “favor” to students long ago. But now that score choice exists, and colleges require official score reports anyway, it is a relic that can put students at a disadvantage if poor scores are shown. I’d sure be complaining loudly if my kids’ school did it.