refactor: rename similar → nearby, so the code says what the section does

The section ranks on distance and is headed "Other schools nearby", but every
identifier still called it "similar" — the exact drift that leaves a later
reader trusting a name over the behaviour.

Mechanical: files, the module, the payload key, the type, the components, the
prop. No behaviour change; the suites are unchanged in count and still green.
Free to do now because #150 has not merged, so the payload key rename needs no
lockstep deploy. Uses of "similar" that are ordinary English — progress
measures compared to similar pupils, and unrelated comments — are untouched.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

nextjs-app/components/school/NearbySchoolsCompareBar.tsx

@@ -0,0 +1,59 @@
+'use client';
+
+/**
+ * The selection count and the one decisive action in the section.
+ *
+ * The CTA is a real link, not a handler: /compare already parses `urns` from
+ * the query string, so the hand-off needs no new compare plumbing. It counts
+ * this school plus whatever the reader ticked, because comparing a shortlist
+ * without the school they are looking at is not what they asked for.
+ */
+
+import Link from 'next/link';
+import { useComparisonContext } from '@/context/ComparisonContext';
+import type { NearbySchool } from '@/lib/types';
+import styles from './NearbySchools.module.css';
+
+export function NearbySchoolsCompareBar({
+  thisUrn,
+  candidates,
+}: {
+  thisUrn: number;
+  candidates: NearbySchool[];
+}) {
+  const { selectedSchools } = useComparisonContext();
+
+  // Only the schools this section offers, in the order the cards show them —
+  // the basket may hold schools picked up elsewhere on the site, and this bar
+  // speaks for this section.
+  const offered = candidates
+    .map((c) => c.urn)
+    .filter((urn) => selectedSchools.some((s) => s.urn === urn));
+
+  const count = offered.length;
+  const href = `/compare?urns=${[thisUrn, ...offered].join(',')}`;
+
+  return (
+    <div className={styles.footer}>
+      <p aria-live="polite">
+        <strong>
+          {count
+            ? `${count} school${count === 1 ? '' : 's'} selected`
+            : 'Compare side by side'}
+        </strong>
+        {count
+          ? 'This school is included automatically.'
+          : 'Add a school to compare it with this one.'}
+      </p>
+      {count ? (
+        <Link className={styles.compare} href={href}>
+          Compare {count + 1} schools →
+        </Link>
+      ) : (
+        <span className={styles.compare} aria-disabled="true">
+          Compare →
+        </span>
+      )}
+    </div>
+  );
+}