These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Tearjerker: Subverted in "Yesteryear" in that when Spock decides that his mortally wounded pet sehlat had to be put down, that is the moment when he embraces the Vulcan way of emotional control and logic.
Played straight in that it's a heartbreaking moment for Amanda; and also to Adult Spock, when he comforts his dying pet.