A government institution cannot promote any one religion. It's fine to have a multi-denominational non-secular common worship area. You can also promote religion as a general concept, but not a specific religion.
Whether this rule is followed or enforced properly is an entirely separate problem that we are apparently still grappling with.
Because they're an authority figure in that context.
Same reason I can flirt with you, but your boss can't.
It’s also in poor taste. Jesus himself commented on performative piety:
“Whenever you pray, do not be like the hypocrites, who love to stand and pray in the synagogues and on street corners so that others may observe them doing so. Amen, I say to you, they have already received their reward. 6 But when you pray, go into your room, close the door, and pray to your Father in secret. And your Father who sees everything that is done in secret will reward you“
This sounds like nobody in a position of power should be allowed to openly do anything that people around them have the right to not do. Which would be kinda bs.
Luckily there are both witness accounts and photos in this case, so it’s pretty clear what was really going on.