At a total solar eclipse the sun is barely covered, like right after sunset. So why is it much darker than right after sunset (which allows us to see the corona)?
The most significant difference is that in a total eclipse the moon obstructs the sun's light outside of earth's atmosphere whereas at sunset, the light is obstructed by the horizon within the atmosphere. With the sun just below the horizon, sunlight still hits the atmosphere above the horizon and even above you, and it's scattered all around.
Even around the total eclipse's trail there's partial shadowing, considerably reducing the amount of sunlight into the atmosphere that could be scattered.
(image from Wikipedia)
Right after you see the sun disappearing below the horizon, the air above you is still illuminated and scatters light back to the ground. That is why it is not completely dark during dusk. During a solar eclipse, the moon casts a shadow on both you and the air above, so there is no scattering going on.
Additionally, its quite a quick change. The moon is doing about 1 km/s orbital velocity, and so is its shadow (approximately)
The length of Dusk can vary, but somewhere between 15-60 minutes at most commonly populated latitudes.
An average adult's horizon is around 5 km away on flat land. So the "edge" of the shadow will pass over an outdoor observer and their surroundings in just 10 seconds. This is not instant, but one's eyes take a period to adjust. Its somewhat akin to turning off a room light and being unable to see anything until one's night vision returns.