loading an blazor app into a new tab requires creating a new blazor instance, and rerunning the authentication logic.
if you are using cookie authentication (blazor server), you can reduce the logic by requiring the blazor hosting page to require authorization. if the original cookie has not expired, it will not need to redirect to the long service. if you are storing jwt tokens, then you want a persistent store keyed by the username key.
if you are using blazor WASM, you can store the authentication tokens in localstorage, and check first at load (need custom authentication state provider).