You wrote your house's security code on a Post-It note. Somebody came in as a houseparty guest and located the note, and discretely copied it onto their hand to get access to the house during your next vacation.

Which verb would describe their knowledge of this security code?

Obtained, read, viewed, learned, discovered.

The knowledge wasn't obtained illegally or illicitly, immorally perhaps.

Illegal entry/trespass is a crime regardless of the method used however.

In your analogy copying the code (online content) isn't necessarily illegal, however using that knowledge without compensation, permission or attribution may be a crime (depending on copyright law, judges rulings etc).

"eavesdropped"?

"spied"?

Whatever it is, slapping "steal" on it because what was done is wrong, and stealing is wrong, is the same sloppy logic that the copyright lobby used in the 80s/90s.

The crime there is using that knowledge illegally to break in.

learned