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/tests/test_school_details.py

@@ -126,3 +126,89 @@ def test_places_names_only_pages_that_exist(monkeypatch):
         assert place["name"]
         assert place["count"] >= 1
         assert place["url"].startswith("/schools/")
+
+
+def _brentwood_df(phase: str = "Primary", n: int = None):
+    from backend.places import MIN_SCHOOLS
+    n = n if n is not None else MIN_SCHOOLS
+    return lambda: pd.DataFrame([
+        {
+            "urn": 100000 + i,
+            "school_name": f"Brentwood School {i}",
+            "town": "Brentwood", "local_authority": "Essex",
+            "postcode": "CM15 8AA", "phase": phase, "year": 202425,
+            "rwm_expected_pct": 60.0, "attainment_8_score": 50.0,
+            "ofsted_grade": 2.0, "ofsted_date": None,
+        }
+        for i in range(n)
+    ])
+
+
+def _places_for(monkeypatch, df_factory, urn: int):
+    from backend import app as app_module
+    monkeypatch.setattr(app_module, "load_school_data", df_factory)
+    monkeypatch.setattr(app_module, "get_supplementary_data", lambda db, urn: {})
+    monkeypatch.setattr(app_module, "_place_registry", None)
+    client = TestClient(app_module.app, raise_server_exceptions=False)
+    return client.get(f"/api/schools/{urn}").json()["places"]
+
+
+def test_a_place_offers_the_phase_page_this_school_appears_on(monkeypatch):
+    # "primary schools in brentwood" is the query the phase pages exist for,
+    # and ~950 of them were once reachable by nothing at all.
+    places = _places_for(monkeypatch, _brentwood_df("Primary"), 100000)
+    town = next(p for p in places if p["kind"] == "town")
+
+    assert town["phases"], "a primary school in a published primary town has a link"
+    assert town["phases"][0]["url"] == "/schools/brentwood/primary"
+    assert town["phases"][0]["count"] >= 1
+
+
+def test_an_all_through_school_offers_both_phase_pages(monkeypatch):
+    # It genuinely appears on both, so there is no tie to break.
+    places = _places_for(monkeypatch, _brentwood_df("All-through"), 100000)
+    town = next(p for p in places if p["kind"] == "town")
+
+    assert {p["phase"] for p in town["phases"]} == {"primary", "secondary"}
+
+
+def test_outcodes_never_offer_a_phase_page(monkeypatch):
+    # The registry gives outcodes no phase route — nobody searches "primary
+    # schools in SW11" — and computing them anyway once put a link to a
+    # nonexistent route on all 1,720 outcode pages.
+    places = _places_for(monkeypatch, _brentwood_df("Primary"), 100000)
+    outcode = next((p for p in places if p["kind"] == "outcode"), None)
+
+    if outcode is not None:
+        assert outcode["phases"] == []
+
+
+def test_a_school_absent_from_the_phase_page_is_not_linked_to_it(monkeypatch):
+    # The check is URN membership in the registry's own phase list, not a
+    # re-derivation of the phase mapping. A secondary school must not be sent
+    # to a primary phase page that does not list it.
+    from backend.places import MIN_SCHOOLS
+
+    def df():
+        rows = [
+            {"urn": 100000 + i, "school_name": f"P{i}", "town": "Brentwood",
+             "local_authority": "Essex", "postcode": "CM15 8AA",
+             "phase": "Primary", "year": 202425, "rwm_expected_pct": 60.0,
+             "attainment_8_score": np.nan, "ofsted_grade": 2.0,
+             "ofsted_date": None}
+            for i in range(MIN_SCHOOLS)
+        ]
+        rows.append({
+            "urn": 900000, "school_name": "Lone Secondary", "town": "Brentwood",
+            "local_authority": "Essex", "postcode": "CM15 8AA",
+            "phase": "Secondary", "year": 202425, "rwm_expected_pct": np.nan,
+            "attainment_8_score": 50.0, "ofsted_grade": 2.0, "ofsted_date": None,
+        })
+        return pd.DataFrame(rows)
+
+    places = _places_for(monkeypatch, df, 900000)
+    town = next(p for p in places if p["kind"] == "town")
+
+    # The town publishes a primary page, but this secondary school is not on
+    # it, and there are too few secondaries for a secondary page.
+    assert town["phases"] == []