With the removal of the old stat.<criterion> scoreboard criteria, the new ones seem to be a bit buggy. Specifically, the change of stat.damageDealt over to minecraft.custom:minecraft.damage_dealt isn't tracking the proper damage values.
To test, simply create a scoreboard objective of type minecraft.custom:minecraft.damage_dealt, show it in the sidebar, and punch something with a bare fist. It logs a damage score of 10. 10 damage would be enough to kill a pig or a cow with a single punch, and obviously that doesn't happen; 10 is much higher than the actual amount of damage dealt (about 10x as much).
Something isn't working right here...
This might be intended, as the scoreboard now tracks smaller damage (when the cooldown didn't run out yet) as well. To test this, use the following command to get a stick with which you can try to murder a mob of your choice:
The scoreboard increases by two everytime you hit a mob.
This might as well be an accidental change though.