docs(docs): add ProblemBadges component, layout slot, and enrich pages with topics/video frontmatter, plus guide placeholders and topic‑landing map.

apps/docs/components.ts

@@ -1,7 +1,7 @@
 /**
- * Project MDX components, available on every page with no import. Static
- * `.astro` files ship no framework JS (a custom element carries any
- * behaviour); interactive React lives in `islands/` instead.
+ * Project MDX components, available on every page with no import, and layout
+ * slot overrides. Static `.astro` files ship no framework JS (a custom element
+ * carries any behaviour); interactive React lives in `islands/` instead.
  */
 import { defineComponents } from "blume";
 
@@ -10,4 +10,8 @@ export default defineComponents({
     Carousel: "./components/Carousel.astro",
     CarouselImage: "./components/CarouselImage.astro",
   },
+  layout: {
+    // Problem pages' topic + explanation badges, from `topics:` / `video:` frontmatter.
+    PageHeader: "./components/ProblemBadges.astro",
+  },
 });