Consistent
loud humming may well be the fuel pump. With the standard DME relay the pump only comes on with engine start, there is no priming, so aligns with what you've said.
As in the comments above, the internal CCU fan can continue for up to 20 mins, so if the noise stops every time the engine is turned off then I don't think its the internal CCU fan.
When the pump was done did any of the fuel filters get replaced? There are two, a 'normal' one in the engine bay and another at the base of the tank, this one is rarely replaced, certainly not routinely.
To test the pump you can use a jumper wire to activate the fuel pump when the car is off, see the first part of this:
https://www.pelicanparts.com/techar...elivery_Tests/20-FUEL-Fuel_Delivery_Tests.htm
If the noise is indeed the pump, I would replace both filters alongside the pump to be sure. The state of the in-tank filter will dictate wether or not you need to 'flush' the tank to remove any varnish or debris.
Hope this helps.