Fix duplicate auth menu: inject fragment in both desktop and mobile sections

Fragment contains responsive desktop/mobile spans. Inject in both
header sections so each span shows at the correct breakpoint.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

templates/_types/root/header/_header.html

@@ -41,9 +41,10 @@
     </div>
   {% endcall %}
   {# Mobile user info #}
-  <div class="block md:hidden text-md font-bold">
-    {# Auth menu mobile — part of auth-menu fragment (id=auth-menu-mobile) #}
-    {% if not auth_menu_html %}
+  <div class="block md:hidden">
+    {% if auth_menu_html %}
+      {{ auth_menu_html | safe }}
+    {% else %}
       {% if g.user %}
         {% include '_types/root/mobile/_full_user.html' %}
       {% else %}