open_stream(), and with it stream::Get() and SSEClient, wrote its own
request head and left out what a buffered request gets: the
Authorization from set_basic_auth() or set_bearer_token_auth(), and
through a plain HTTP proxy the absolute-form target (RFC 9112 3.2.2)
and Proxy-Authorization. A proxy refused such a request, and an origin
that needs credentials answered 401.
Move the two decisions out of write_request() and handle_request() into
add_credential_headers() and proxy_target_prefix(), and use them in
open_stream() too, after connecting as a buffered request does. A
Digest challenge or a redirect is still handed to the caller.