fix(api): treat "16 plus" as secondary, the way PHASE_GROUPS already does

GIAS phase 6 is "16 plus", and PHASE_GROUPS deliberately files it in the
secondary group. The payload helper decided the same question with
`"secondary" in phase_text`, which that value does not satisfy — so a
sixth-form college was handed the primary bucket and offered infant schools
as its peers, with the KS2 metric key to label them. No crash; just a page
confidently showing the wrong schools.

The decision now lives in similar_schools.is_secondary_phase, beside the
PHASE_GROUPS bucket it selects from, so the two cannot drift again. A test
pins them together.

The same binary assumption had a second output. computeSchoolFlags tests for
the substring too, so a 16-plus school renders the primary template, and the
composer was labelling the section from the template: "Other primary schools
near <sixth form college>" above a row of secondaries. The section now
derives its noun from the school's own phase, which also removes the
duplicated wording from both composers. A 16-plus school's candidates span
the whole secondary group, so no single noun fits and it gets the honest
general one.

Reported in review on #150.

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

backend/tests/test_similar_schools.py

@@ -11,7 +11,7 @@ set, never far enough to fill the last of the six slots.
 import numpy as np
 import pandas as pd
 
-from backend.similar_schools import select_similar
+from backend.similar_schools import is_secondary_phase, select_similar
 
 # Roughly 0.7 miles apart in latitude at this longitude.
 BASE_LAT, BASE_LON = 51.5000, -0.1000
@@ -203,6 +203,38 @@ def test_all_through_is_offered_on_both_phase_sides():
     assert 100002 in {s["urn"] for s in select_similar(secondary, 100010, is_secondary=True)}
 
 
+def test_sixteen_plus_is_matched_against_secondary_not_primary():
+    """GIAS phase 6 is "16 plus", and PHASE_GROUPS puts it in the secondary
+    group — a sixth-form college's peers are secondaries and other colleges,
+    never primary schools. A substring test for "secondary" misses it silently:
+    no crash, just a page offering infant schools to a sixth form."""
+    frame = _frame(
+        _row(100001, "Sixth Form College", phase="16 plus", age_range="16-19"),
+        _row(100002, "Nearby Secondary", phase="Secondary", latitude=_at(0.5),
+             attainment_8_score=52.0),
+        _row(100003, "Nearby College", phase="16 plus", latitude=_at(0.6),
+             attainment_8_score=np.nan),
+        _row(100004, "Nearby Primary", phase="Primary", latitude=_at(0.1)),
+    )
+    result = select_similar(frame, 100001, is_secondary=is_secondary_phase("16 plus"))
+    urns = {s["urn"] for s in result}
+    assert 100004 not in urns, "a primary school is not a peer for a sixth form"
+    assert urns == {100002, 100003}
+    assert all(s["metric_key"] == "attainment_8_score" for s in result)
+
+
+def test_is_secondary_phase_agrees_with_the_phase_groups_it_selects_from():
+    """The two must not drift: whatever this calls secondary decides which
+    PHASE_GROUPS bucket the candidates come from."""
+    for phase in ("Secondary", "Middle deemed secondary", "16 plus"):
+        assert is_secondary_phase(phase) is True, phase
+    for phase in ("Primary", "Middle deemed primary", "Nursery", "", None):
+        assert is_secondary_phase(phase) is False, phase
+    # In PHASE_GROUPS an all-through school is on both sides, but it renders
+    # with the primary template, and the metric follows the template.
+    assert is_secondary_phase("All-through") is False
+
+
 def test_chips_state_only_what_the_tier_earned():
     frame = _frame(
         _row(100001, "Subject", phase="Secondary", gender="Mixed",