Is believing/faith a work ?
Again, yes it is. Its the action, function, deed of the mind, the soul, and heart. The word work ergon means:
work, labor, action, deed,
/érgon ("work") is a deed (action) that carries out (completes) an inner desire (intension, purpose)
Phillip told the ethiopian eunuch Acts 8:37
And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
So if one bases their Salvation on believing, their act, they are basing it on their works, no way around it !