Most devotion skills will count in both main-hand and off-hand (right-hand and left-hand) weapon damage. Even the tooltip does not show off-hand / left-hand damage, it is truely counted in. Only 3 exceptions, Scorpion, Assassin and Korvaak. Their common feature is that they belong to the same skill type, AttackProjectileRing.
As a comparison, AttackProjectileBurst, a highly similar type, including Bat and Falcon, does count in off-hand weapon damage.
Testing Details:
I use mod to change skill damage to fixed 1000% Weapon Damage and 0 other damage. In my case, if off-hand / left-hand weapon damage is counted in, the dummy will take ~30k damage. Otherwise, if not counted in, the dummy will take less than 20k damage.
My off-hand weapon can also cause debuff on dummy (main-hand cannot). So debuff icon appears if counted in.
Results:
Scorpion, Assassin and Korvaak do lower damage and no debuff icons. Others do higher damage and show debuff icons.
_
BTW, here is another off-hand / left-hand weapon damage bug (maybe).
Some modifiers give Replicating Missile and DEE weapon damage, Slathsarr’s Crest, Groble Toxic Effigy and etc.
When casting the two skills, character will use 3 possible animations, right-hand casting, left-hand casting and both-hand casting. For right-hand casting and both-hand casting, only main-hand / right-hand weapon damage is counted in, while for left-hand casting, only off-hand / left-hand weapon damage is counted in.
Most DEE builds and Missile builds use a focus off-hand, which has 0 weapon damage. This means the actual value of weapon damage modifiers is much lower than the paper value.
Tests are similar, off-hand / left-hand uses a debuff weapon, and only left-hand casting can cause debuff icon.
left-hand:
right-hand:
double-hand: