Fifteen day's LWOP (Leave Without Pay) is no joke. It's not a "Slap on the wrist". It's actually very high on the disciplinary scale for a government employee. Besides the monetary loss, this is a career killer in any personnel jacket.
No cares given about the impact of the discipline. I doubt it is near a career killer.
Fact is She is still a snot slinging bureaucrat that will be worse because of "Muh Feels" were hurt.
In the end, this paragraph tells the probable real reason of the suspension.
"She snapped a photo and promptly posted it on the official Alaska State Commission for Human Rights website with the caption, “In what world is this okay?” She did this on state computers, on state time on an official state of Alaska social media page. As though her position allows her to regulate Alaskans’ free speech rights. "
Had it not been on state time and equipment, an eyebrow would have never been raised. She is already high enough in the .gov that promotion may not be a question. Her career will likely suffer very little, if at all.