My car just started doing this two days ago, which made me remember reading this thread.
I fixed it, I think, by going into service mode and putting each parking brake into service position. (I think it's called EPB Service Mode, for when you're replacing the rear brake pads) This fully retracts and engages each parking brake, taking it through the full range of motion. After I did this, the squeal/squeak stopped immediately when putting the vehicle into Park. This is probably the "Calibration" that the service center did on OP's car. But it's not listed as a calibration, it just takes the EPB to both extremes.
I'll update if it comes back. My guess is that the full unwinding of the parking brake screw stirred up some grease and re-distributed it on the threads. My car only has 22k on it, there's no reason for it to need new calipers so soon.
And yeah - there's no logic to brake fluid or a caliper slide lubrication service changing this sound. The noise is coming from the EPB motor.