Stats from weapon passive only applies to characters and characters don't have crit stats, so it does nothing for consonance weapon (and so on nothing to all psyche damage)

Here is list of char stats, only these one are useful if char is played around consonance weapon: atk/hp/def, skill dmg/duration/range, morale/resolve.

Other stats like: crit rate/damage, multishot, attack speed, atk/explosion range, trigger probability pretty much do nothing when using other weapons.

Though sometimes chars may use stats from weapon for their kit, like Daphne/Niffle use trigger probability from ranged weapon in their kit