Why does this MOSFET switch on so slowly?
I thought that this kind of MOSFET was a switch


Well, it is a transistor, just like a BJT. It might have been designed optimized for either being totally pinched off or fully on, but that doesn't mean it doesn't have a relative gate voltage range in between those two extremes.


  which I expected to saturate immediately.


A MOSFET's gate needs to be charged, i.e. it works like one half of a capacitor.

Now, with a charging current of 3.55 pA, that might take a while – with a datasheet saying it has a total gate charge of ca 67 nC, a little more than 5 hours to fully charge. (It doesn't work that way, because capacitor charge curves don't lead to constant current, but it's an initial estimate).