refactor(cli): generate docs/site.json manifest and update docs site references

apps/cli/videos.ts

@@ -3,8 +3,8 @@
  * Find the NeetCode explanation video for every docs page that has none.
  *
  * A finished solution page carries frontmatter `video: <YouTube id>` —
- * NeetCode's walkthrough of the problem — which the docs MDX `wrapper`
- * (`apps/docs/components/ProblemBadges.astro`) renders as the red
+ * NeetCode's walkthrough of the problem — which the site's MDX `wrapper`
+ * (prdlk/cs `components/ProblemBadges.astro`) renders as the red
  * "Explanation" badge beside the topic badges. `sync.ts` never writes that key
  * (it owns `icon:`, `topics:` and `## Solution`), so pages accumulate without
  * one. This script lists every numbered page lacking `video:` and looks each
@@ -25,7 +25,7 @@ import { join } from "node:path";
 import { printTable } from "./report.ts";
 import { ROOT } from "./work.ts";
 
-const DOCS = join(ROOT, "apps", "docs", "content");
+const DOCS = join(ROOT, "docs");
 const WRITE = process.argv.includes("--write");
 
 /** Channel handles searched in order; the first exact match wins. */