Suburban sf-30 furnace noise after shutting down

Typically, when thermostat has been satisfied that temperature has reached setpoint, there is no power available to furnace. When you replaced the thermostat there may still exist a constant power to part of the furnace.
A meter on the furnace circuits may diagnose this condition. Probes placed on the limit switch is where I would be looking. You may also have a wonky limit switch but I don't know if that would cause an "electronic noise" as you have described.