am I missing some way of seeing
from the battalion inventory screen?
- what a character's Authority skill is (directly, not just by inferring from what battalions are greyed out), and
- what my character's currently-equipped battalion's Authority requirement is
Your authority skill is on the same screen with stuff like swords, Faith, riding, etc, it's another skill you can work on with higher authority giving you more accuracy with gambits and unlocking skills that make your gambits stronger/more endurance/bonus skills.
Just like weapons you can only lead a battalion if your authority is a high enough level. If you look at your list of battalions either in the inventory or the guild master you can see what rank they require from E to S (I dunno if there are any s rank battalions).
You can see your armies authority skill on teaching days or by looking at the class roster in the menu and going to the skills page.