There's no action. The check is automatically made by all party members when combat starts, and then again once the enemy is killed (because of experience gained fighting them or from investigating the dead body). Importantly, the check is made again when you encounter an enemy for the 2nd, 3rd, etc time, making it likely that you'll know something about the enemy by the 2nd encounter. Additional successful checks and/or higher rolls on those checks would give you more information: abilities, saving throws, lore. It rewards putting points into nature and/or arcana and makes you feel like you're learning more about enemies as you face them.
It would also tie in well to a bestiary, which is really something that BG3 should have. Encountering enemies would slowly fill out your bestiary which you could look at any time.
I don't know, that seems just tedious. How do I figure out how likely I am to hit:
* Check the bestiary and do some quickmaths - boring, plus, I am playing a video game, the game should do it for me
* The chance to hit appears after successful checks - now we implemented a good qol feature, but locked it behind some random rolls.
Plus, why would killing an enemy with say Thunderwave or any Save spell reveal its AC. Maybe we should only reveal a creatures AC to the companion that killed it, only if they killed it with an attack and only if they succeeded on a check...
This is a game, and we are going to make abstract rules. So why not make those rules simple?