Rosemary is a flavor, not a nutrient source. A tablespoon of fresh chopped rosemary is about 2 calories, and nobody eats enough of it for the numbers on this page to change their day.
Rosmarinic acid and carnosic acid are real compounds and they are genuinely studied, mostly in cell and animal work, and mostly at concentrations far above what a sprig in a hot pan delivers.
This page used to say rosmarinic acid may support cognitive function, focus and memory retention. No large human trial supports that, it is a claim about how your brain works, and it was carrying no source. It is gone, and the change is logged on the corrections page.
The practical reason to reach for rosemary is that it holds up to long cooking where soft herbs collapse, so it can go in at the start of a roast rather than at the end.