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/lib/format.ts

@@ -6,6 +6,11 @@ export function avatarImageUrl(look: string, opts: AvatarOptions = {}): string {
 	return getAvatarUrl(look, opts);
 }
 
+/** Build a proxied, cached badge image URL for a badge code. */
+export function badgeImageUrl(code: string): string {
+	return `/api/imaging/badge?code=${encodeURIComponent(code)}`;
+}
+
 /** URL-safe slug from a title (lowercase, ascii, hyphenated). */
 export function slugify(input: string): string {
 	// NFKD splits accented letters into base + combining mark; the combining