Implement in C# HTTP Client Requests an authentication process in a web app that uses token from external authority and uses digital signature for authentication

I have a C# .NET framework 4.8 Windows Forms Application that interacts with a website using digital signature and Web Requests. I need to integrate an external auth provider that issues a token and I need to get that token and attach it to requests. The external auth provider uses a digital signature to sign the login requests, and issues the token that needs to be captured. We need proficiency in using tools like Fiddle to understand all requests and replies, and replicate them in the C# code with HTTPClient / HTTPRequests and similar, since all must be executed in background. I would prefer to avoid using of external tools or libraries like Selenium. I will pay until the login is finished and the application is returning valid responses (not error pages because of authentication). I can do demonstrations using shared screen apps before bidding. Attaching a very small sample of code and the Authentication Schema that must be implemented. The external Digital Signature local application is already working, that part IS NOT required.
KEYWORDS: C# + Fiddle + HTTPClient + HTTPRequests + Cookies + FormData + JavaScript + API