fix(school): send the school page its admissions policy, and read it exactly

The header's Selective flag read school_info.admissions_policy, which the
detail endpoint never sent, so no school page could flag Selective while
its search row did (staging E2E: The Grammar School at Leeds). The detail
payload now carries it, and a contract test checks it carries every field
the header's flags read.

Sending it would have switched on two older copies of the tag logic #176
fixed in the rows. The Admissions section and the cut-off note both tested
includes('selective'), so every non-selective secondary would have read
"entry is by selective examination". The section also counted "None" as a
faith: Burntwood reads "a faith-based admissions priority (None)" today.
All of them now share isSelective() and hasReligiousCharacter(), which also
treats "Not applicable" as no faith, as the place table already does.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

backend/app.py

@@ -1047,6 +1047,8 @@ async def get_school_details(request: Request, urn: int):
             "age_range": latest.get("age_range", ""),
             "has_sixth_form": latest.get("has_sixth_form"),
             "nursery_provision": latest.get("nursery_provision"),
+            # The header's Selective flag reads it (lib/schoolFacts).
+            "admissions_policy": latest.get("admissions_policy"),
             "status": latest.get("status"),
             "latitude": latest.get("latitude"),
             "longitude": latest.get("longitude"),

backend/tests/test_school_page_flag_fields.py

@@ -0,0 +1,55 @@
+"""The school page's header flags (nextjs-app/lib/schoolFacts.ts) read seven
+school_info fields, so the detail payload must carry every one.
+
+It lacked admissions_policy, so no school page could flag Selective while its
+search row did: Tiffin and The Grammar School at Leeds showed the tag in
+search and nothing on their own pages.
+"""
+
+import numpy as np
+import pandas as pd
+import pytest
+from fastapi.testclient import TestClient
+
+# The fields schoolFlags() picks from School (FlagFields in lib/schoolFacts.ts).
+FLAG_FIELDS = (
+    "type_group", "admissions_policy", "gender", "religious_denomination",
+    "nursery_provision", "has_sixth_form", "phase",
+)
+
+
+def _school_df() -> pd.DataFrame:
+    return pd.DataFrame([{
+        "urn": 136910, "school_name": "Tiffin School", "phase": "Secondary",
+        "school_type": "Academy converter", "admissions_policy": "Selective",
+        "gender": "Boys", "religious_denomination": "Christian",
+        "nursery_provision": "Not applicable", "has_sixth_form": True,
+        "age_range": "11-18", "local_authority": "Kingston upon Thames",
+        "address": "Queen Elizabeth Road, Kingston upon Thames, KT2 6RL",
+        "postcode": "KT2 6RL", "latitude": 51.41, "longitude": -0.30,
+        "year": 202425, "attainment_8_score": 75.0, "total_pupils": 200,
+        "gias_total_pupils": 1478, "ofsted_grade": np.nan,
+    }])
+
+
+@pytest.fixture()
+def client(monkeypatch):
+    from backend import app as app_module
+
+    monkeypatch.setattr(app_module, "load_school_data", _school_df)
+    monkeypatch.setattr(app_module, "load_latest_school_data", _school_df)
+    monkeypatch.setattr(app_module, "get_supplementary_data", lambda db, urn: {})
+    monkeypatch.setattr(app_module, "_place_registry", None)
+    return TestClient(app_module.app, raise_server_exceptions=False)
+
+
+def test_the_school_page_carries_every_field_its_flags_read(client):
+    resp = client.get("/api/schools/136910")
+    assert resp.status_code == 200, resp.text
+    info = resp.json()["school_info"]
+    assert [f for f in FLAG_FIELDS if f not in info] == []
+
+
+def test_the_school_page_says_a_selective_school_is_selective(client):
+    info = client.get("/api/schools/136910").json()["school_info"]
+    assert info["admissions_policy"] == "Selective"