What do you think?
I think it depends on the camera, with some of the newer cameras caring little whether you expose correctly in camera or adjust afterwards.
Here is a shot I took recently. Both were taken from the same setup and within minutes (seconds even) of each other, with the only difference being the ISO setting, one being at ISO400, the other at ISO4000.
They were also processed identically, with the only difference being that the ISO400 shot's exposure was lifted by 3 1/3rd stops, so that the total exposure is the same. Post processing was done in Lightroom, and the camera is a D500.
Personally, I can see no difference in the stars/background, and possibly a little more detail in the foreground of the ISO400 shot...
I had the same experience with my previous camera, the D750.
To my mind, if you need a set shutter speed and aperture, and you are shooting one of the late-model Nikkors, you may as well shoot at base ISO. The only problem with doing so is that it may become impossible to see sharpness on the LCD.