docs(docs): add wrapper badge component, make backlinks collapsible, and include solution code for Gas Station problem

apps/docs/components/BacklinksList.astro

@@ -15,10 +15,14 @@
  *
  * Problem pages are recognised by their `<num>. <name>` title, the shape
  * `apps/cli/sync.ts` writes.
+ *
+ * The list is a native `<details>`, open on load: the chevron at the top
+ * right of the header row collapses it like an accordion, with no JS.
  */
 import { getEntry } from "astro:content";
 import data from "blume:data";
 import { withBase } from "blume/components/islands/base-path.ts";
+import Icon from "blume/components/Icon.astro";
 import { tagTarget, type TopicTag } from "../topic-landings.ts";
 
 interface Props {
@@ -61,11 +65,17 @@ const backlinks = problems.some((p) => p.route.path === route)
 
 {
   backlinks.length > 0 && (
-    <section aria-labelledby="backlinks" class="not-prose mx-auto mt-12 max-w-content border-border border-t pt-6">
-      <h2 class="mb-2 flex items-baseline gap-2 font-medium text-muted-foreground text-xs uppercase tracking-wide" id="backlinks">
-        Backlinks
-        <span class="tabular-nums">{backlinks.length}</span>
-      </h2>
+    <details
+      class="group not-prose mx-auto mt-12 max-w-content border-border border-t pt-6"
+      open
+    >
+      <summary class="mb-2 flex cursor-pointer list-none items-center justify-between gap-2 text-muted-foreground transition-colors hover:text-foreground [&::-webkit-details-marker]:hidden">
+        <h2 class="flex items-baseline gap-2 font-medium text-xs uppercase tracking-wide" id="backlinks">
+          Backlinks
+          <span class="tabular-nums">{backlinks.length}</span>
+        </h2>
+        <Icon class="shrink-0 transition-transform group-open:rotate-180" name="chevron-down" size={16} />
+      </summary>
       <ul class="text-sm">
         {backlinks.map((p) => (
           <li>
@@ -79,6 +89,6 @@ const backlinks = problems.some((p) => p.route.path === route)
           </li>
         ))}
       </ul>
-    </section>
+    </details>
   )
 }