First and foremost, please add the following line to the .dpr of your project and also to the .dpr of WebClient.web project in the Sphinx demos.
begin
Application.HandleOAuth := False; // ADD THIS LINE
Application.Initialize;
This should make the existing demo to work, after this latest break in TMS Web Core.
Make sure the demo is working fine.
Once you confirm the demo is working, please go back to your project, add the same line, and please provide the details of what's happening after that fix is added.