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

apps/docs/content/guides/binary-tree.mdx

@@ -0,0 +1,8 @@
+---
+title: "Binary Tree"
+list: "https://leetcode.com/problem-list/binary-tree/"
+---
+
+:::note
+This guide has not been written yet. The LeetCode list above has every problem tagged Binary Tree.
+:::