The Pope’s manuscript
Nope. But the next day’s NYTimes reported that it was a replica (hence, not actually a manuscript) of a copy of a legal text by Jacob ben Asher. Now I can’t find that report, and instead it says it is a replica of a manuscript from circa 1435. (So it probably isn’t Vatican Ebr. 151, a Byzantine manuscript from the 14th-15th century with Kitzur Piske ha-Rosh, by R. Jacob ben Asher).
As you may know, a new and comprehensive catalogue of the Hebrew manuscripts in the Vatican libraries is on the way. Meanwhile, I checked the IMHM catalogue and found only two Vatican manuscripts dated 1435. One of them, Rossiana 555, is a copy of Rabbi Jacob ben Asher’s major work, the Tur. It was copied in Italy and contains decorations of some sort, making it a likely candidate for the gift (for a short description of the manuscript, see here, at the end of the ‘Text’ section).