interactive auto is a server static render pre-render with a WASM client. if login is to be handled by the WASM client without a redirect, then you need to write custom authentication.
the build-in authentication uses razor pages and cookie authentication. the Blazor app redirects to the razor pages to login and set the cookie. the SSR renders to the client via pre-render persist state the user principal:
https://learn.microsoft.com/en-us/aspnet/core/blazor/components/prerender?view=aspnetcore-9.0
the other option with WASM is oauth and msal which requires requires the Blazor code redirect to the oauth server to get the id token.
if you are using individual accounts, you can write custom authenication. your SSR server will need to supply a webapi to login via a passed user name & password, and return the user principal in some format. if the WASM will make other api calls, then a JWT token would be handy, but you could use a custom header.
the Blazor login page would call the webapi to login, then call the custom authentication state provider and pass the new user principal information.
note: Blazor WASM does not support SigninManager. it needs to call a webapi. If you switched to Blazor Server you could use it.