Does Thalia, Guardian of Thraben make activated abilities cost more?

Thalia, Guardian of Thraben reads: "Noncreature spells cost {1} more to cast." The operative word is spells — specifically spells cast from a player's hand or wherever they originate. Activated abilities are explicitly not spells under the rules.

CR 113.1 defines abilities and distinguishes them from spells. CR 602.1 explains that activating an ability follows a specific process separate from casting a spell. Because activated abilities are never "cast," Thalia's tax does not apply to them at all.

This means that even if an artifact or land has an activated ability with a mana cost in its activation cost (e.g., "{2}: Draw a card"), Thalia does not make that ability cost {3} instead. Only the act of casting a noncreature spell from hand (or elsewhere) is taxed.

Concrete example: Your opponent controls Thalia. You want to activate Arcane Signet's ability ({T}: Add one mana of any color in your commander's color identity). You pay only {T} as written — Thalia adds nothing, because you are activating an ability, not casting a spell.

If instead you wanted to cast a noncreature spell like Counterspell ({U}{U}), you would need to pay {U}{U}{1} thanks to Thalia's effect, since that is a noncreature spell being cast (CR 601.2, 601.2f).