What counts as "adding" a piece (e.g., adding an Invader for Confounding Mists)?

What counts as "adding" a piece (e.g., adding an Invader for Confounding Mists)?

A new piece getting placed on the board.
In the Confounding Mists case, this most commonly occurs due to a Build or Explore action, but can also happen due to Events, Adversary effects, or Scenarios.
Pieces that are pushed, gathered, brought, or otherwise moved then count as "moved," but not "added." Replacing one piece with another (or multiple others) counts as neither adding nor moving the new pieces; while the pieces representing that entity have changed, the entity itself is not a new arrival.