While figuring it out on why the authentication in the console client demo ceased to work property, I found several other issues.
These were related generally to switching list parameter mapping for Iri templates to OData. This spec uses variables lie $top or $skip for queries. Unfortunately, it came out that the $ char is not compatible with the Url template spec - it had to be escaped with % as a hex number. It was also incompatible with ExpandoObject I used for passing variables for the template, which I had to replace with the IDictionary. I don’t have to mention that these variables were not covered in the tests.
Few other minor pips and boobs here and there and finally it started to work.
I have to have some rest as the final thing is left here - hypermedia controls handling.