The narrator's use of the adjective "ecstatically" in the line " 'do they
miss me? ' she cried ecstatically" conveys that:

The use of the word "ecstatically" in that line conveys that she is happy that who ever "they" is cares about her and is thinking about.

Explanation:

Imagine you left school for a week, and your friend texts and says "Your crush said hi" Then you would say "Does he miss me?" all excited, cus that would mean your crush is thinking about you.

often a noun phrase is just a noun or a pronoun:

people like to have money.

i am tired.

it is getting late.