The only major difference (in regards to code organisation) between Unity's old classes and ECS is that in Unity the logic ("Systems") is coupled with the data

The only major difference (in regards to code organisation) between Unity's old classes and ECS is that in Unity the logic ("Systems") is coupled with the data ("Components") in the same class. Entities in Unity are already not concrete implementations (probably just a "handler" ID) as far as the user is concerned. This is pretty much like ECS.