docs(docs): add BacklinksList component and shared tagTarget logic for badge routing, update docs pages

apps/docs/components/ProblemBadges.astro

@@ -10,33 +10,23 @@
  *   topic tags. A tag the campaign teaches (`topic-landings.ts`) links to that
  *   topic's landing page and reads accent; any other tag links to its guide
  *   page, `/guides/<slug>` (sync creates one per such tag), and reads neutral.
+ *   `tagTarget()` picks the route (and between two landings, e.g. DFS); the
+ *   `PageFooter` backlinks list reads the same answer.
  * - `video:` (problem pages, written by `apps/cli/videos.ts`) is the NeetCode
  *   walkthrough's YouTube id, the red "Explanation" badge at the end of the row.
  * - `list:` (guide pages, written by sync on create) is the tag's LeetCode
  *   problem list, an orange "LeetCode list" badge.
- *
- * A tag naming two campaign topics (`Depth-First Search` is both Tree DFS and
- * Graph DFS) links to the page's own topic — its route's first segment — when
- * that is one of them; otherwise DFS/BFS prefer the tree topic for a problem
- * LeetCode also tags `Tree` and the graph topic for the rest. A route the site
- * does not serve (a landing or guide page removed) falls back to LeetCode's
- * problem list for the tag, so a badge never links to a 404.
  */
 import { getEntry } from "astro:content";
 import data from "blume:data";
 import Badge from "blume/components/content/Badge.astro";
 import { withBase } from "blume/components/islands/base-path.ts";
-import { TOPIC_LANDINGS } from "../topic-landings.ts";
+import { tagTarget, type TopicTag } from "../topic-landings.ts";
 
 interface Props {
   route: string;
 }
 
-interface TopicTag {
-  name: string;
-  slug: string;
-}
-
 const { route } = Astro.props;
 const at = data.routes.find((r: { path: string }) => r.path === route);
 const entry = at ? await getEntry(at.collection, at.entryId) : undefined;
@@ -44,17 +34,12 @@ const tags: TopicTag[] = entry?.data.topics ?? [];
 const video: string | undefined = entry?.data.video;
 const list: string | undefined = entry?.data.list;
 
-const served = new Set(data.routes.map((r: { path: string }) => r.path));
-const own = `/${route.split("/")[1]}`;
-const prefer = tags.some((t) => t.slug === "tree") ? "/tree-" : "/graph-";
+const served = new Set<string>(data.routes.map((r: { path: string }) => r.path));
 
 const badges = tags.map((tag) => {
-  const landings = (TOPIC_LANDINGS[tag.slug] ?? []).filter((path) => served.has(path));
-  const landing = landings.includes(own) ? own : (landings.find((p) => p.startsWith(prefer)) ?? landings[0]);
-  if (landing) return { name: tag.name, href: withBase(landing), accent: true, external: false };
-  const guide = `/guides/${tag.slug}`;
-  if (served.has(guide)) return { name: tag.name, href: withBase(guide), accent: false, external: false };
-  return { name: tag.name, href: `https://leetcode.com/problem-list/${tag.slug}/`, accent: false, external: true };
+  const target = tagTarget(tag, { route, tags }, served);
+  const external = target.kind === "external";
+  return { name: tag.name, href: external ? target.href : withBase(target.href), accent: target.kind === "landing", external };
 });
 
 const linkClass = "no-underline transition-opacity hover:opacity-80";