feat(skills-hub): health checks, freshness badge, and a watchdog cron (#32345)

Layered safety so the Skills Hub at /docs/skills stays in sync without
silent rot. Three pieces:

1. build_skills_index.py — refuses to ship a degenerate index.
   EXPECTED_FLOORS per source (skills.sh ≥100, lobehub ≥100, clawhub ≥50,
   official ≥50, github ≥30, browse-sh ≥50) and MIN_TOTAL=1500. Any source
   collapsing to zero (the silent OpenAI breakage that hid for weeks) now
   fails the workflow loud — broken index never reaches the live site.

2. extract-skills.py + the React page — visible freshness signal.
   Sidecar website/src/data/skills-meta.json carries the index's
   generated_at timestamp, plus per-source counts. Skills Hub renders a
   'Catalog refreshed N hours ago · auto-rebuilt twice daily' line under
   the hero copy. If the cron stalls, users see the staleness immediately.

3. .github/workflows/skills-index-freshness.yml — watchdog cron.
   Every 4 hours, fetches the live /docs/api/skills-index.json, validates
   shape, checks age (>26h is stale), checks the same per-source floors,
   and opens (or appends to) a GitHub issue when anything is off. The
   issue is title-prefixed [skills-index-watchdog] so subsequent failures
   append a comment instead of spamming new issues.

Net effect:
- A silent regression like 'OpenAI tap moved its skills' now fails the
  build instead of shipping a quietly broken catalog.
- A stuck cron (like the landingpage breakage that ran red for weeks) now
  files an issue within 4 hours.
- Users see how fresh the catalog is on the page itself.

Test plan:
- Local: built skills-meta.json from the live index → 'Catalog refreshed
  N minutes ago' rendered correctly in the static HTML.
- Probe logic dry-run against the live index: total=2456, all 6 sources
  above floor, age 0.1h — issues=NONE.
- Triggered skills-index.yml manually; both jobs green, deploy-site.yml
  dispatch fired.

website/src/pages/skills/index.tsx

@@ -1,6 +1,7 @@
 import React, { useState, useMemo, useCallback, useRef, useEffect } from "react";
 import Layout from "@theme/Layout";
 import skills from "../../data/skills.json";
+import meta from "../../data/skills-meta.json";
 import styles from "./styles.module.css";
 
 interface Skill {
@@ -24,6 +25,33 @@ interface Skill {
 
 const allSkills: Skill[] = skills as Skill[];
 
+interface IndexMeta {
+  extractedAt?: string;
+  indexGeneratedAt?: string;
+  totalSkills?: number;
+  externalSource?: string;
+  bySource?: Record<string, number>;
+}
+const indexMeta: IndexMeta = meta as IndexMeta;
+
+function formatRelativeTime(iso?: string): string | null {
+  if (!iso) return null;
+  const then = new Date(iso).getTime();
+  if (!Number.isFinite(then)) return null;
+  const now = Date.now();
+  const diffMs = now - then;
+  if (diffMs < 0) return "just now";
+  const mins = Math.floor(diffMs / 60_000);
+  if (mins < 1) return "just now";
+  if (mins < 60) return `${mins} minute${mins === 1 ? "" : "s"} ago`;
+  const hours = Math.floor(mins / 60);
+  if (hours < 24) return `${hours} hour${hours === 1 ? "" : "s"} ago`;
+  const days = Math.floor(hours / 24);
+  if (days < 30) return `${days} day${days === 1 ? "" : "s"} ago`;
+  const months = Math.floor(days / 30);
+  return `${months} month${months === 1 ? "" : "s"} ago`;
+}
+
 const CATEGORY_ICONS: Record<string, string> = {
   apple: "\u{f179}",
   "autonomous-ai-agents": "\u{1F916}",
@@ -487,6 +515,17 @@ export default function SkillsDashboard() {
               <strong className={styles.heroAccent}>{allSkills.length}</strong> skills
               across {sources.length - 1} registries
             </p>
+            {(indexMeta?.indexGeneratedAt || indexMeta?.extractedAt) && (
+              <p className={styles.heroSub} style={{ fontSize: "0.85rem", opacity: 0.75 }}>
+                Catalog refreshed{" "}
+                <span title={indexMeta.indexGeneratedAt || indexMeta.extractedAt}>
+                  {formatRelativeTime(
+                    indexMeta.indexGeneratedAt || indexMeta.extractedAt,
+                  ) || "recently"}
+                </span>
+                {" "}· auto-rebuilt twice daily
+              </p>
+            )}
 
             <div className={styles.statsRow}>
               <StatCard