This is the site for purchasing images through L’Osservatore Romano, the Vatican newspaper. Their photographers follow the Holy Father throughout his day and travels. They are certainly reputable. I don’t know if they are considered the “Vatican” photographers or if this is another group. I know when you visit the Vatican there is an office in Vatican City to purchase images from the Popes audiences, etc. I am not sure whether this is the same office.
I am sure you would get a good quality image with photo.va, though I have not purchased from them myself. I am just not sure how long it would take to receive it. I have often thought of ordering from them because you can get an original photograph that is more unique than some of the mass produced images.