Mystery! I have been chasing a water leak and I have isolated every loop in the house and the leak is less but still present. I have even had the water dept change out the meter.

I had the water cut off to a bathroom to fix a dripping faucet & while replacing the seat & spring I heard my electric water heater making thumping noises and about 1/2 gallon of water came out of the COLD (not hot) faucet that I had open working on.

I quickly went upstairs to the heater and it was making a noise as if water were running. I cut off the supply valve to the heater and it still made the noise. After about 5 minutes or less it quit.

Why would an electric hot water heater do this when there was no usage and the water supply cut off?

While you were working, so was your water heater. The thermostat on the heater 'called' for heat and so the element was energized. That began a warming (thumping sound, absent when the water heater is pressurized) of the water which in turn expanded the volume of the water that resulted in your getting a gush out your open faucet. Good luck with tracing down the leak.

Correct. The thermostat turned the element on, the water expanded as it heated. Thus the thumping sound and expelled water.