For posterity, all sprites in all animation clips used in an Animator Controller will be pre-loaded into memory.
In other words, it’s not a good idea to have all of your animations for a character handled by one Animator Controller if you have lots of animations for that character.
In my case, (2D point and click adventure game), I’m going to have to either break my controllers apart, or start using the Playables API (probably via some third party library like Animancer).
I wish this were documented somewhere, so here’s my wish being granted! Hope this helps someone else.