I think if this was a transactional type of task (i.e. making a purchase of something) then a confirmation page would be your 'happy state' because after the purchase/checkour page you will get the confirmation page/message.
However, for a non-transactional type of task there really isn't a page that shows completion of task (since you never undertook one), so I don't think there would be anything like this.
If we are talking about it from the designer's perspective, rather than using a subjective term of whether the user is happy or not, it is preferable to use a term like 'ideal state' or path for the user flow that you are guiding the user towards. From the user's perspective, they might not necessarily be 'happy' to have completed the task either (e.g. it might be to pay a fine), so it is better to use a more neutral term for this.