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/NearbySchoolsCarousel.tsx

@@ -0,0 +1,127 @@
+'use client';
+
+/**
+ * The scroller and its arrows.
+ *
+ * `children` are the server-rendered cards and `header` the server-rendered
+ * heading and lede: both stay server components, passed through, so this file
+ * owns a DOM ref and nothing else. That is what keeps all six links in the
+ * initial HTML — a carousel that mounted cards on click would put four of the
+ * six beyond a crawler and beyond a reader with no JavaScript.
+ *
+ * With JavaScript off this degrades to a horizontally scrollable row, which is
+ * still usable by touch and trackpad.
+ */
+
+import { useCallback, useEffect, useRef, useState, type ReactNode } from 'react';
+import styles from './NearbySchools.module.css';
+
+/** Three cards fit the row, so fewer than four has nowhere to scroll to.
+ *  Below 640px the arrows are not rendered at all — see the stylesheet. */
+const VISIBLE = 3;
+
+/**
+ * Why a tolerance rather than `=== 0`.
+ *
+ * The scroller carries 2px of padding so focus rings are not clipped, and
+ * scroll-snap treats that padding as the first card's snap position — a row at
+ * rest reports scrollLeft 2, not 0. Sub-pixel rounding moves it again at other
+ * zoom levels. An exact test leaves the back arrow live on first paint,
+ * pointing nowhere.
+ */
+const EDGE = 8;
+
+export function NearbySchoolsCarousel({
+  count,
+  labelledBy,
+  header,
+  children,
+}: {
+  count: number;
+  labelledBy: string;
+  header: ReactNode;
+  children: ReactNode;
+}) {
+  const scroller = useRef<HTMLUListElement>(null);
+  const [atStart, setAtStart] = useState(true);
+  const [atEnd, setAtEnd] = useState(false);
+  const scrollable = count > VISIBLE;
+
+  const sync = useCallback(() => {
+    const node = scroller.current;
+    if (!node) return;
+    const max = node.scrollWidth - node.clientWidth;
+    setAtStart(node.scrollLeft <= EDGE);
+    setAtEnd(node.scrollLeft >= max - EDGE);
+  }, []);
+  // `atEnd` is not only the forward arrow's disabled state: below 640px, where
+  // no arrow is rendered, it is the only thing driving the scroll-fade.
+
+  // Also on mount: the first measurement can only happen once there is layout.
+  useEffect(sync, [sync]);
+
+  const page = (direction: 1 | -1) => {
+    const node = scroller.current;
+    if (!node) return;
+    // A page is what the reader can see, so the viewport is the step.
+    node.scrollBy({ left: direction * node.clientWidth, behavior: 'smooth' });
+  };
+
+  return (
+    <>
+      <div className={styles.top}>
+        {header}
+        {scrollable && (
+          <div className={styles.arrows}>
+            <button
+              type="button"
+              className={styles.arrow}
+              onClick={() => page(-1)}
+              disabled={atStart}
+              aria-label="Previous schools"
+            >
+              <Chevron direction="prev" />
+            </button>
+            <button
+              type="button"
+              className={styles.arrow}
+              onClick={() => page(1)}
+              disabled={atEnd}
+              aria-label="More schools"
+            >
+              <Chevron direction="next" />
+            </button>
+          </div>
+        )}
+      </div>
+
+      <ul
+        ref={scroller}
+        className={styles.scroller}
+        onScroll={sync}
+        data-at-end={atEnd}
+        {...(scrollable
+          ? { tabIndex: 0, role: 'group', 'aria-labelledby': labelledBy }
+          : {})}
+      >
+        {children}
+      </ul>
+    </>
+  );
+}
+
+function Chevron({ direction }: { direction: 'prev' | 'next' }) {
+  return (
+    <svg
+      viewBox="0 0 24 24"
+      fill="none"
+      stroke="currentColor"
+      strokeWidth="2"
+      strokeLinecap="round"
+      strokeLinejoin="round"
+      aria-hidden="true"
+    >
+      <path d={direction === 'prev' ? 'M15 18l-6-6 6-6' : 'M9 18l6-6-6-6'} />
+    </svg>
+  );
+}