feat(seo): link school pages into the location layer

W2 shipped ~5,000 place pages and nothing linked into them. The
location layer pointed down at school pages; school pages pointed
nowhere on the site. Their only anchor was the school's own website, so
the ~27k pages carrying most of the site's inbound authority passed it
straight off-site, and the new corpus was reachable mainly through the
sitemap.

Three things close the loop.

A reverse index over the place registry, places_for_urn, answers which
published places contain a school. Derived from the registry rather
than stored beside it, so the two cannot disagree about which places
exist: a place below the publish threshold is absent from the registry
and therefore never offered as a link. A test asserts that invariant
across every place in a built registry.

GET /api/schools/{urn} gains a `places` array carrying the name, count
and canonical path for each. It rides on the request the page already
makes, so the school page costs no extra round trip. The frontend types
it optional and defaults it to empty, because the two images deploy
separately and a frontend ahead of the API must render without it.

The page gains a "More schools near here" module and a BreadcrumbList.
The module orders narrowest first, because a reader on a school page
wants its town before its county, while the API orders widest first for
the trail. Anchors state their destination's size — "37 schools in
Brentwood" — which is worth more to a reader and a crawler than "see
more". With no published places it renders nothing rather than an empty
heading.

The trail is rooted at the homepage, not /schools. There is no /schools
index page; the location layer lives only at /schools/[place],
/schools/authority/[la] and /schools/near/[outcode]. Rooting it at the
bare path would have opened every breadcrumb with a link to a 404.
Outcodes are omitted from the trail: "schools near CM15" is a real
query and a useful link, but nobody navigates Essex to CM15 to a
school, and a breadcrumb claiming that describes a hierarchy the site
does not have.

School pages also now declare the School type rather than
EducationalOrganization, the parent type that covers universities and
nurseries alike.

The e2e journey asserts the round trip in both directions, following a
place page's own first school so the pair is genuinely related rather
than hardcoded. A one-way link is what already existed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01DXnXQKnPpZBBP61fBQiFkq

e2e/tests/journeys.spec.ts

@@ -1935,6 +1935,50 @@ async function firstPlaceOfKind(page: Page, kind: string) {
   return hit as { kind: string; slug: string; name: string; count: number };
 }
 
+/**
+ * The round trip. Place pages always linked down to school pages; school
+ * pages linked nowhere on the site, so the ~27k of them that carry most of
+ * the inbound authority stranded it — their only anchor pointed at the
+ * school's own website.
+ *
+ * Asserting both directions is the point. A one-way link is what already
+ * existed and is not what this journey is for.
+ */
+test('a school page links back into the location layer, and the place page links down', async ({ page }) => {
+  const town = await firstPlaceOfKind(page, 'town');
+
+  // Start from the place page and take its first school, so the pair is
+  // guaranteed to be genuinely related rather than a hardcoded guess.
+  await page.goto(`/schools/${town.slug}`);
+  const schoolHref = await page.locator('a[href^="/school/"]').first()
+    .getAttribute('href');
+  expect(schoolHref, 'the town page listed no school to follow').toBeTruthy();
+
+  await page.goto(schoolHref!);
+
+  // Down: the school page must offer a link back to the town it sits in.
+  const backToTown = page.locator(`a[href="/schools/${town.slug}"]`);
+  await expect(backToTown).toHaveCount(1);
+  await expect(backToTown).toBeVisible();
+
+  // The anchor says what it leads to, which is worth more than "see more".
+  await expect(backToTown).toContainText(town.name, { ignoreCase: true });
+  await expect(backToTown).toContainText(/\d+ schools?/);
+
+  // And the breadcrumb resolves the school into a real hierarchy.
+  const blocks = await page.locator('script[type="application/ld+json"]')
+    .allTextContents();
+  const graph = blocks.join(' ');
+  expect(graph).toContain('"BreadcrumbList"');
+  // The narrower type, not the EducationalOrganization parent it used to be.
+  expect(graph).toContain('"School"');
+
+  // Following it lands on a real page, not a 404.
+  await backToTown.click();
+  await page.waitForURL(new RegExp(`/schools/${town.slug}$`));
+  await expect(page.locator('h1')).toContainText(town.name, { ignoreCase: true });
+});
+
 for (const [kind, prefix, article] of [
   ['town', '/schools/', 'a'],
   ['authority', '/schools/authority/', 'an'],