One way to do it is to just lay some foam out on a heavy steel table. Then there's a tool that is pretty much two sharpened pipes welded inside of each other.

You use it as a hole punch. Put it on the foam and wack it with a hammer. Cut's perfect donuts. You can make your own tool and make your own foams on the cheap. Got a few in the garage for certain things. Thinwall steel tubing works well.

Maybe the bigger tire co.s have a simple punch press for this.

I'm sure there is even weirder ways to make foam donuts I'm missing......
I think some of the shaped foams are injection molded foam. Two dies get filled with allmost liquid foam, then clamped together giving that weird seam.