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)/1d-dynamic-programming/70-climbing-stairs.mdx

@@ -2,13 +2,15 @@
 title: '70. Climbing Stairs'
 description: You are climbing a staircase. It takes n steps to reach the top
 icon: dot
+topics:
+  - { name: "Math", slug: "math" }
+  - { name: "Dynamic Programming", slug: "dynamic-programming" }
+  - { name: "Memoization", slug: "memoization" }
 sidebar:
   label: 'Climbing Stairs'
   badge: 'Easy'
 ---
 
-<Badge variant="accent">Math</Badge>
-
 ### Example 1:
 - Input: `n = 2`
 - Output: `2`