"That means if we switch on an electric bulb it should turn on after 17 mins. But we can turn on the electric bulb in our home at a lightning speed with a flick of a switch. This is because the speed of the electric current does not depend on the drift velocity of the electron.

Electric current moves with a speed of light. It is not established with the drift velocity of the electrons in the material. Thus, it may vary in material but the speed of electric current always established on the speed of light."

https://www.elprocus.com/drift-velocity-of-electrons-with-derivation/

Interesting read.