I can't find an official ruling other than reading the description of existing wands/staves/rods (
https://www.aidedd.org/dnd-filters/magic-items.php).
Those descriptions always seem to indicate "while holding" before explaining the magical effect(s) of those "weapons".
Which, sounds logical to me : not only are those items probably the arcane focus (which needs to be held to cast spells) of the character trying to throw it, but they would most probably be the focus of the magic they hold.
However, it
indeed would be great if they updated the description for this staff (and many other objects) to be more accurate and avoid confusion.
