feat(site): fetch the GitHub star count at build time

Read stargazers_count once per build and expose it both raw and rounded.
Deploy previews build from shared, unauthenticated IPs, so GitHub's rate
limit is a routine answer rather than an incident: any failure falls back
to a constant instead of breaking the build.

website/.vitepress/githubStars.data.ts

@@ -0,0 +1,64 @@
+import { defineLoader } from 'vitepress';
+
+const REPO = 'go-task/task';
+
+// Deploy previews build from shared, unauthenticated Netlify IPs, so a 403 from
+// GitHub's 60 requests/hour limit is routine. Falling back keeps the build green
+// with a number that is only ever too low.
+const FALLBACK_STARS = 16000;
+
+export interface GithubStars {
+  count: number;
+  label: string;
+}
+
+declare const data: GithubStars;
+export { data };
+
+export default defineLoader({
+  async load(): Promise<GithubStars> {
+    const count = await fetchStarCount();
+    return { count, label: formatCount(count) };
+  }
+});
+
+async function fetchStarCount(): Promise<number> {
+  const headers: Record<string, string> = {
+    Accept: 'application/vnd.github+json'
+  };
+  if (process.env.GITHUB_TOKEN) {
+    headers.Authorization = `Bearer ${process.env.GITHUB_TOKEN}`;
+  }
+
+  try {
+    const response = await fetch(`https://api.github.com/repos/${REPO}`, {
+      headers,
+      signal: AbortSignal.timeout(5000)
+    });
+    if (!response.ok) {
+      throw new Error(`GitHub answered ${response.status}`);
+    }
+
+    const { stargazers_count } = await response.json();
+    if (typeof stargazers_count !== 'number') {
+      throw new Error('no stargazers_count in the response');
+    }
+    return stargazers_count;
+  } catch (error) {
+    console.warn(
+      `Could not read the star count for ${REPO} (${error}), falling back to ${FALLBACK_STARS}.`
+    );
+    return FALLBACK_STARS;
+  }
+}
+
+// Rounding is deliberate: a count that never shows its last digits cannot look
+// stale between two deployments.
+function formatCount(count: number): string {
+  return new Intl.NumberFormat('en', {
+    notation: 'compact',
+    maximumFractionDigits: 1
+  })
+    .format(count)
+    .replace('K', 'k');
+}