An entry in the Codex may be warranted. In the mean time, to point you towards support in the existing documentation:
Page 9 of the Academy book clearly defines an Activation as when a Creature takes an Action.
Arena cards and rules don't tend to reference Activation, preferring instead to use Action Phase as you're familiar with. Page 11 of the Arena rules though does describe an Activation as "First, choose a creature and activate it: Flip over its action marker to the inactive side, and remove its guard marker (if any). Now you are ready to act with it! Choose one of the 3 options below. Your creature can either:" Take a move + quick action, take a full action, or do nothing.
It is a bit more ambiguous in its wording, but you should interpret all of that, i.e. the entire Action Phase, as the Activation. The description doesn't completely exclude interpretation as just meaning Activating the creature, but such an interpretation wouldn't make sense as that doesn't provide any opportunity to do anything else. As soon as you're done flipping the Action Marker, you've activated the creature. There's just no time during that to do anything else as it starts and ends with the Action Marker being flipped. The only interpretation that makes sense is that the entirety of the text, including acting with the creature, is describing an Activation, which also aligns much better with it's more obvious meaning within Academy.