fix: group header actions

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

frontend/src/components/AppHeader.vue

@@ -48,10 +48,10 @@ const modeLabel = computed(() => {
         <span class="mode" :class="{ failed: healthFailed }">
           {{ modeLabel }}
         </span>
+        <AuthStatus :auth="auth" @logout="$emit('logout')" />
         <a v-if="demoUrl" class="button demo-link" :href="demoUrl">
           {{ messages.appHeaderDemoInstance }}
         </a>
-        <AuthStatus :auth="auth" @logout="$emit('logout')" />
         <button class="button" type="button" data-dev-panel-opener @click="openDevPanel">
           <span class="full-label">
             {{ messages.appHeaderDevPanel }}