Is happy a predicate adjective

No, the Word 'joyful' is an adjective. An adjective that follows a linking verb and renames or modifies a subject is called a predicate adjective.

Example: Mary is joyful about the news.

A predicate noun is a noun or a pronoun that follows a linking verb and renames or modifies a subject.

Example: Mary is my sister.

Both a predicate noun and a predicate adjective are called a subject complement.