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/package.json

@@ -11,6 +11,7 @@
   },
   "dependencies": {
     "@fortawesome/fontawesome-svg-core": "^7.3.1",
+    "@fortawesome/free-brands-svg-icons": "^7.3.1",
     "@fortawesome/free-solid-svg-icons": "^7.3.1",
     "@fortawesome/vue-fontawesome": "^3.3.3",
     "@tanstack/vue-table": "^8.21.3",