client/web: always run platform auth for login mode

Even if connected to the login client over tailscale, still check
platform auth so the browser can obtain the tokens it needs to make
platform requests complete successfully.

Updates #10261

Signed-off-by: Sonia Appasamy <sonia@tailscale.com>

client/web/web.go

@@ -406,7 +406,7 @@ func (s *Server) serveAPIAuth(w http.ResponseWriter, r *http.Request) {
 
 	session, whois, err := s.getSession(r)
 	switch {
-	case err != nil && errors.Is(err, errNotUsingTailscale):
+	case s.mode == LoginServerMode || errors.Is(err, errNotUsingTailscale):
 		// not using tailscale, so perform platform auth
 		switch distro.Get() {
 		case distro.Synology: