Ward, the new keyword introduced in Strixhaven, counters spells and abilities that target that creature unless you pay a cost.
Ward {2} (Whenever this creature becomes the target of a spell or ability an opponent controls, counter it unless that player pays {2}.)
Now, Baral, Chief of Compliance says this:
Whenever a spell or ability you control counters a spell, you may draw a card. If you do, discard a card.
Does the Ward keyword count as an ability for the purposes of Baral's draw ability?