From what I can tell, a scenario where this can happen is when ArcGIS Pro consumes a hosted feature layer, e.g. https://portal.domain.local/server/rest/services/Hosted/layer1/FeatureServer. It thinks there's an associated map service (there isn't - hosted feature layers don't have corresponding map services) and makes a request to a map service that doesn't exist, i.e. https://portal.domain.local/server/rest/services/Hosted/layer1/MapServer, which triggers the error.
I'm trying to get confirmation on this. I'll post a follow up with what I find out.