Staves only get a boost from 2 handed when used as melee weapons, which I'm sure you've discovered, should be pretty rare after the very start of the game.

Since the recent update, tenebrium damage does not switch a weapon to the exclusive purview of the Tenebrium ability. For the bow, it would continue to benefit from the bow ability, with an extra bonus damage from tenibrium. Change to Tenebrium in v251

Here is a wiki page on Traits.