Same issue on docker container (which is dotnet core too) proget.inedo.com/productimages/inedo/proget:5.3.11
I see the same issue when doing a docker push :

received unexpected HTTP status: 500 Internal Server Error

When I catch the HTTP response to PUT /v2/base/alpine/manifests/3.9 HTTP/1.1 with wireshark I can read : Could not find a part of the path '/var/proget/packages/.docker/F3'.
Also since I did a bind mount in the docker I can see that the folder F3 is not created : /var/proget/packages/.docker/F3

But docker push works with the docker image proget.inedo.com/productimages/inedo/proget:5.3.10
And F3 folder is created as expected and I can find the manifest.

@ben Thank you so much I spend a lot of times searching for that. Should it be in proget docker installation documentation (in HTTPS Support section) ? Thank again.
My setup docker client > HAProxy > Proget. Also don't forget to add a HTTP frontend that redirects to HTTPS frontend in HAProxy.