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

apps/docs/content/(05-decision-space)/backtracking/46-permutations.mdx

@@ -2,13 +2,14 @@
 title: '46. Permutations'
 description: Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order
 icon: dot
+topics:
+  - { name: "Array", slug: "array" }
+  - { name: "Backtracking", slug: "backtracking" }
 sidebar:
   label: 'Permutations'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Array</Badge>
-
 ### Example 1:
 - Input: `nums = [1,2,3]`
 - Output: `[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]`