I'm working with ArcGIS Pro 1.4.1 and Portal for ArcGIS 10.3.1 (Federated with Server)
I've been able to connect to Portal through ArcGIS Pro and publish Web Maps and Web Layers to it just fine.
I've attempted to 'Overwrite Web Layer' but I get the error message 'Overwriting is not supported to your portal':
I haven't been able to find any other instances of this error in GeoNet or Google. I am able to overwrite services in ArcMap.
I notice here that 'Currently, ArcGIS Pro only supports overwriting web feature layers that do not reference registered data.' - does this mean Map Images cannot be overwritten at all, regardless of where the data comes from? This might be true, but the error message above points to a bigger issue.
I did encounter this issue when I was trying to overwrite our cadastral editing web layer. Deleting the portal connection and re-adding the portal connection and logging in again did the trick.
Mind you I am working in ArcGIS Pro 2.9.2