D&D 5E Are Heavy Weapons really their own category?

[GameDoc]

You can add finesse weapons to the discussion of "category vs. property".

I looked over the table again and I note that the dagger, quarterstaff, and shortsword are classified as finesse weapons, meaning clerics (including war clerics) can't use them.

So now clerics can't use quarterstaffs. However, the Staff of Stiking description notes that clerics can attune to the item to use its magical properties.

The dagger and quarterstaff should be a basic weapons and the short sword a martial one, it seems to me (in addition to being finesse weapons).