Better mod tools. From a moderator (not admin) PoV:
modmail
ability to tag users and annotate things about them, preferably in a way that is visible for the rest of the mod team
a list of the most recent comments+posts in the community EDIT - already there, as pointed out by ericjmorey. I feel dumb for not noticing it before.
some sort of automatic warning, based on keywords
Specifically for the desktop browser interface (IDK how much it applies to other interfaces), it would be great if the [M] for moderator was a tiny bit less evident when you’re just posting/commenting as a user, but there was a stronger highlight when speaking officially. Plenty times I feel the need to start the comment with [speaking as a mod], as that shield icon is easy to miss.
For admins I can’t speak personally, but the list Beehaw admins provided seems IMO sensible.