Refactor tmdbImageUrl to accept semantic category instead of size string

- Change primary argument from TMDB size string (`w500`, `w1280`, etc.)
  to category name (`posters`, `backdrops`, `stills`, `logos`,
  `profiles`); optional size override remains as third argument
- Update all call sites across services, actions, pages, and route
  handlers to use the new category-based API
- Update image.test.ts to match the new signature and replace
  size-mapping test descriptions with category-name descriptions

app/page.tsx

@@ -23,7 +23,7 @@ const posterPaths = [
 ];
 
 const posterUrls = posterPaths
-  .map((p) => tmdbImageUrl(p, "w300"))
+  .map((p) => tmdbImageUrl(p, "posters", "w300"))
   .filter(Boolean) as string[];
 
 export default function Home() {