fix(seo): build the phase links the docstring already promised

Review caught _places_payload documenting a `phase_url` the function
never returned. The docstring was not stray prose: the approved design
included the phase variant — "Primary schools in Beccles" was one of
its four example links — and it was dropped during implementation
without being mentioned. Deleting the sentence would have closed the
report while losing the feature, so the links are built instead.

These are the pages that most needed them. ~950 phase variants were
once reachable by nothing at all: absent from every sitemap and
unlinked from the place page. "Primary schools in brentwood" is the
query they exist to answer.

Membership is read from the registry's own `phase_urns` rather than
re-derived from the school's phase string. The registry already decides
which phases a place publishes and which schools are listed on each, so
asking it is both shorter and the only way the link cannot disagree
with the page it points at. It also means outcodes need no special
case: they carry empty `phase_urns` by design, because nobody searches
"primary schools in SW11", so they report no phase links on their own.

`phases` is a list rather than a single url. An all-through school is
listed on both the primary and secondary pages, so there is no tie to
break and no reason to invent one. Each entry renders directly after
its own place, so "22 primary schools in Brentwood" reads as part of
Brentwood rather than as an unrelated link further along the row.

The e2e journey now follows a phase link where the town publishes one
and asserts it resolves.

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

backend/app.py

@@ -216,20 +216,37 @@ def _places_payload(urn: int) -> list[dict]:
     them: a name to write in the link, a count so the anchor can say what it
     leads to, and the canonical path.
 
-    `phase_url` is present only where the place publishes a page for this
-    school's phase, which is the registry's decision alone — repeating the
-    threshold rule here is how the page and the sitemap would come to disagree.
+    `phases` carries the phase variants this school actually appears on, which
+    is usually one and is two for an all-through school — it is listed on both
+    pages, so there is no tie to break.
+
+    Membership is read straight from the registry's own `phase_urns` rather
+    than re-derived from the school's phase string. The registry is the one
+    place that decides which phases a place publishes and who is on them;
+    computing it a second time here is how a page comes to link a school to a
+    phase page that does not list it, or to a route that does not exist. That
+    is also why outcodes need no special case: they carry empty `phase_urns`,
+    so they report no phase links on their own.
     """
     payload = []
     for place in places_for_urn(get_place_registry(), int(urn)):
-        entry = {
+        phases = [
+            {
+                "phase": phase,
+                "count": len(phase_urns),
+                "url": f"{_place_url(place)}/{phase}",
+            }
+            for phase, phase_urns in sorted(place.phase_urns.items())
+            if int(urn) in phase_urns
+        ]
+        payload.append({
             "kind": place.kind,
             "slug": place.slug,
             "name": place.name,
             "count": len(place.urns),
             "url": _place_url(place),
-        }
-        payload.append(entry)
+            "phases": phases,
+        })
     return payload