It's not clear what you do as you provide almost no code to demonstrate your issue. However, it is very clear what you're striving at.
In order to authenticate and authorize users in Blazor WebAssembly App you can use Jwt authentication or OpenID connect that pass a user's credentials to a Web Api end points to verify the users, create a Jwt token, and pass it back to the front end where you can store the Jwt Token in the local storage, and retrieve it when the user logs in, accesses various resources, etc.
Note also that the HttpClient is not really the actual HttpClient. It is based on the JavaScript Fetch Api, and it is missing features like WebSockets, etc.
I've posted in this section answers about how to use Jwt Authentication and OpenID Connection. You'll have to search for those answers dealing with Jwt Authentication, as it was relatively long time ago, and I don't remember their locations. However, here is the links to Adding OpenID Connect to IdentityServer4, and Accessing token from Blazor
Hope this helps...