I’m not sure why there is no clear explanation about how to find this token. Blazor Server should not use the HttpContext (per Microsoft), so all the examples out there do not apply. I think something the .net devs should do is add a token handler to the auth state provider like they do for the web assembly side.
I might also add that if there is a concern about exposure of the token to the client side, you could store in memory instead of claims.