You’re talking about two different things though.
1- it’s more energy efficient to wash dishes in a dishwasher, than to wash them by hand. It seems that the data backs this up.
2- it’s wasteful to run a less than full dishwasher. This is obvious because you’re using the same resources to wash fewer dishes.
A dish soap manufacturer is pushing people to run a less than full dishwasher, but that doesn’t mean that switching to hand washing is a better choice either. It just means that ideally you’d wait until it is full and run it.
What’s the cutoff point? Seems like it’s somewhere between 8 dishes and a full load. But we also need to balance how we live, we should try to not be wasteful, but also realistically, just wash your dishes when they need washing.
You’re being overly aggressive here, and arguing for a completely different point than was initially made.