fix(imaging): make avatar and badge images resilient to upstream outages

- Add persistent disk cache for rendered avatars/badges (storage/imaging)
  so repeats never touch the flaky local renderer and cached renders
  survive upstream downtime
- Serve cache-first with stale-on-error; cut primary/fallback timeouts
  from 10s/6s to 4s/4s so failing images cannot stall pages
- Avatar proxy now returns a graceful 200 silhouette instead of 502 when
  no renderer can produce a figure, so no broken-image glyphs appear
- Badge endpoint becomes a caching proxy trying configured CDN, public
  Habbo CDN and local /swf copy in order, and drops the fragile IP rate
  limit that could blank badge streams
- Route all site badge images (profile, me, badges, apply pages) through
  the cached proxy instead of hot-linking images.habbo.com

src/app/(site)/badges/page.tsx

@@ -17,8 +17,8 @@ export async function generateMetadata(): Promise<Metadata> {
 	};
 }
 
-// Canonical Habbo badge image CDN. A badge_key (e.g. "ADM") maps to a .gif here.
-const BADGE_IMG_BASE = "https://images.habbo.com/c_images/album1584";
+// A badge_key (e.g. "ADM") maps to a .gif served through the cached proxy.
+const BADGE_IMG_BASE = "/api/imaging/badge?code";
 
 export default async function BadgesPage() {
 	const t = await getTranslations("pages.badges");
@@ -50,7 +50,7 @@ export default async function BadgesPage() {
 							>
 								{/* eslint-disable-next-line @next/next/no-img-element */}
 								<img
-									src={`${BADGE_IMG_BASE}/${badge.badgeKey}.gif`}
+									src={`${BADGE_IMG_BASE}=${encodeURIComponent(badge.badgeKey)}`}
 									alt={badge.badgeName}
 									title={badge.badgeKey}
 									width={40}