Right. Having done further reading, my understanding is that what's tagged as the culvert (which should be tagged waterway=pressurised + tunnel=flooded instead of culvert I suspect) is the outlet which is horizontal pipe permitting flow through the dam controlled by a drain gate near bottom of the reservoir. There is a riser with a trash rack which is what is visible there in the water. It is the service/primary spillway and connects to same pipe to regulate reservoir releases additional to the outlet.

As for the featured mapped as spillway: Reviewing FEMA Watershed Models and Floodplain Mapping, at each of the damn sites Milroy1812 has mapped a spillway that corresponds to a Special Flooding Hazard Area zone leading me to believe that they are the auxiliary/emergency spillways.  From my reading, earthen damns built during the era these were often just used vegetated / earth emergency spillways like this that can best be approximated by a broadcrested weir.