feat(webui): redesign admin key gate

Add a circular key-icon badge and a small "LLM Gateway" wordmark, so the
screen reads as this product's door and not a generic prompt.

Restructure the dense security paragraph into a short description plus a
three-item muted checklist. Each claim keeps its original strength: the
key stays in this tab's session storage, the browser never writes it to
disk, and requests go only to this page's own /admin/api/* routes.

Add a show/hide toggle for the key input. It reuses the ghost
icon-button composition SearchInput.vue already uses for its clear
button. Autofocus the input on mount. Disable submit while the trimmed
input is empty.

Add a brief shake on the key input when auth.error is set. The
animation respects prefers-reduced-motion and lives in a scoped
<style> block local to this file — the first one in webui/src/components,
added because no Tailwind-core or tw-animate-css keyframe reads as
"rejected".

Extend the header in App.vue with a GitHub repository link, per an
operator scope addition mid-task: an icon-only ghost button that opens
github.com/lukaszraczylo/traefik-llmgateway in a new tab. The link sits
in App.vue's header, above the gate/dashboard switch, so it renders on
every screen including the auth gate. Installs
@fortawesome/free-brands-svg-icons, pinned like the other fontawesome
packages, for the faGithub icon.

auth.submit() semantics, dashboard.refresh() timing, and the backend
stay unchanged.

webui/src/App.vue

@@ -1,9 +1,11 @@
 <script setup lang="ts">
+import { faGithub } from '@fortawesome/free-brands-svg-icons'
 import { faCircleExclamation } from '@fortawesome/free-solid-svg-icons'
 import { computed, defineAsyncComponent, onMounted, ref } from 'vue'
 
 import AuthGate from '@/components/AuthGate.vue'
 import OverviewView from '@/components/OverviewView.vue'
+import { Button } from '@/components/ui/button'
 import { Tabs, TabsContent, TabsList, TabsTrigger } from '@/components/ui/tabs'
 import UsageView from '@/components/UsageView.vue'
 import { useAuthStore } from '@/stores/auth'
@@ -15,6 +17,10 @@ import { useDashboardStore } from '@/stores/dashboard'
 // lean; it fetches once, on first visit to the Charts tab.
 const ChartsView = defineAsyncComponent(() => import('@/components/ChartsView.vue'))
 
+/** The module path (go.mod / .traefik.yml `import:`) — same repo the plugin
+ * ships from, so this is the one canonical URL rather than a guess. */
+const GITHUB_REPO_URL = 'https://github.com/lukaszraczylo/traefik-llmgateway'
+
 const auth = useAuthStore()
 const dashboard = useDashboardStore()
 
@@ -34,7 +40,21 @@ onMounted(() => {
 <template>
   <div class="flex w-full flex-col gap-6 px-4 py-8 sm:px-6 lg:px-8">
     <header class="flex flex-col gap-1">
-      <h1 class="text-xl font-semibold tracking-tight">LLM Gateway &mdash; Admin</h1>
+      <div class="flex items-center justify-between gap-2">
+        <h1 class="text-xl font-semibold tracking-tight">LLM Gateway &mdash; Admin</h1>
+        <Button
+          as="a"
+          :href="GITHUB_REPO_URL"
+          target="_blank"
+          rel="noopener noreferrer"
+          variant="ghost"
+          size="icon"
+          aria-label="GitHub repository"
+          class="text-muted-foreground hover:text-foreground"
+        >
+          <FontAwesomeIcon :icon="faGithub" class="size-4" aria-hidden="true" />
+        </Button>
+      </div>
       <p class="flex items-center gap-1.5 text-sm text-muted-foreground">
         <FontAwesomeIcon v-if="dashboard.error" :icon="faCircleExclamation" class="size-3.5 text-destructive" />
         <span :class="dashboard.error ? 'text-destructive' : undefined">{{ statusText }}</span>