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

apps/docs/content/(03-hierarchical)/binary-search-tree/98-validate-binary-search-tree.mdx

@@ -2,13 +2,17 @@
 title: '98. Validate Binary Search Tree'
 description: Given the root of a binary tree, determine if it is a valid binary search tree (BST)
 icon: dot
+topics:
+  - { name: "Tree", slug: "tree" }
+  - { name: "Depth-First Search", slug: "depth-first-search" }
+  - { name: "Binary Search Tree", slug: "binary-search-tree" }
+  - { name: "Binary Tree", slug: "binary-tree" }
+video: "s6ATEkipzow"
 sidebar:
   label: 'Validate Binary Search Tree'
   badge: 'Medium'
 ---
 
-<Badge variant="accent">Tree</Badge>
-
 ### Example 1:
 - Input: `root = [2,1,3]`
 - Output: `true`
@@ -62,7 +66,3 @@ class Solution:
 
         return valid(root, float("-inf"), float("inf"))
 ```
-
-## Explanation
-
-<YouTube id="s6ATEkipzow" title="Validate Binary Search Tree - Depth First Search - Leetcode 98" />