As you said, it's the gradient which matters. The gradient determines how much the sea level changes over a distance. But, the sea level change is distinct from

As you said, it's the gradient which matters. The gradient determines how much the sea level changes over a distance. But, the sea level change is distinct from the tides. The difference in water level between two connected locations at the same moment in time is the same for the ocean and the lake. The video you linked to compares lakes and oceans because the lunar tides vary with time. The lake level difference between Cleveland and Buffalo at 6 will be the same as the sea level difference between New York and Providence at ~5:30. You need to compare your sea level to the sea level a quarter of the way around the world to understand why your local sea level changes from 6:00 to 12:00.