So when it says "è la sua", there is the article "la" because it is referring to the pasta not to the person? So rather than saying (in english) "The pasta on the plate is her pasta", they shorten it by saying "è la sua" and removing pasta?
Trying to understand why it's "è la sua" now when sometimes it is just "è sua"
Part of the problem is that the possessive adjectives in Italian and the possessive pronouns are both his/hers, So it’s hard to see the difference in usage. An easier way to understand it is using my and mine Because in English they are different words. So the possessive adjective will be in front of the noun for example la mia pasta = my pasta. At the end following è it is la mia = is mine. This is a more economical way to say the pasta is my pasta. Now just go back and substitute his in the sentence. As has been noted in other comments, at the end of the sentence after a version of the verb essere The use of the definite article is optional so it could be è la sua or è sua.