feat(seo): rewrite the C1 snippets to earn the click (W8)

The baseline says these pages already rank and are not clicked. 'compare
school performance' sits at position 6.1 with 0.43% CTR; 'compare schools' at
7.2 with 0.87%. The brand query 'school compare' draws 9.16% from the same
neighbourhood of the same results page, which rules out a ranking explanation
— when the snippet gives a reason to click, it gets clicked.

These SERPs are owned by the DfE's own 'Compare school performance' service.
The old title put a lowercase brand nobody searches for in the most valuable
pixels, then a near-paraphrase of that service's name. Beside the government's
own result it read as a lookalike.

Intent in the title, differentiator in the description. Titles now match what
people type, and the descriptions carry the one fact gov.uk does not publish:
how close you had to live to get a place.

/compare deliberately takes the tool phrasing rather than the homepage's, so
the two pages stop competing for one phrase. The root layout's default and
Open Graph copy were saying something different again; they now agree.

No hard school counts in any of it. The corpus moves with every data refresh
and this repo has already shipped one copy bug of that kind.

Tests guard the mechanics — SERP length, intent keyword, the differentiator,
no brand-first title — and leave the wording free to iterate.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015mWQnpye9F299NVRCCSRvj

nextjs-app/app/page.tsx

@@ -34,8 +34,21 @@ interface HomePageProps {
  * saying the brand twice.
  */
 export const metadata: Metadata = {
-  title: { absolute: 'schoolcompare | Compare every school in England' },
-  description: 'Search and compare school performance across England',
+  /*
+   * Intent in the title, differentiator in the description.
+   *
+   * These queries are owned by the DfE's own "Compare school performance"
+   * service, and the old title — brand first, then a near-paraphrase of that
+   * service's name — gave a searcher no reason to pick us over it. It drew
+   * 0.43% CTR at position 6.1 while the brand query drew 9.16% from the same
+   * neighbourhood, so the ranking was never the problem.
+   *
+   * The title now matches what people type. The description carries the one
+   * fact gov.uk does not publish: how close you had to live to get a place.
+   */
+  title: { absolute: 'Compare Schools Side by Side | schoolcompare' },
+  description:
+    'Put five English schools on one screen — SATs, GCSE results, Ofsted grades, and how close you had to live to get a place. Free, no sign-up.',
   // This page reads eleven search params. They filter a result set; they do
   // not make a new document. Collapsing every combination onto "/" stops the
   // homepage competing with itself for its own head terms.