Is there a way I can update my custom fields after a file upload (and having obtained the new content Id) using the sn-client-dotnet?
I am targeting a SN 7 installation.
I think you should reload the content, modify the field and call & await saveAsync()
var uploadedDocument = await Content.LoadAsync(uploadedDocId);
uploadedDocument["CustomFieldName"] = someValue;
await uploadedDocument.SaveAsync();
You can find some detailed examples here