Ok, I think I've figured it out! See the flanged bushing inside the oil pump drive?
View attachment 469557
It is supposed to have the flange on the inside!
View attachment 469558
If you install it with the flange on the outside, the flange will contact the clutch shoes, thereby also turning the clutch drum! I reassembled it, and now it idles down to 2800 rpm without the chain turning. I don't remember ever taking that part out of the saw, but maybe I did at some point. Never too old to learn something new!