What is the purpose of heavy cream in a mushroom duxelle?
The heavy cream is basically protein and fat, with some water which you're cooking off.

I think the cream is there to bind, as the mushrooms will probably not quite "stick" well enough.

It also adds to the volume of the completed paté.

Last, but not least, I have been told that cream is tasty. It's there, among other things, to add to the flavour.