fix(seo): submit only school pages that have something to show

Drops the schools with neither results nor an Ofsted grade, adds /admissions
which was never listed, replaces the invented priority and changefreq with a
lastmod taken from each school's Ofsted date.

lastmod is omitted where no date is known rather than defaulted to now. An
always-now lastmod is a claim Google learns to distrust; absent honestly
means unknown.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015mWQnpye9F299NVRCCSRvj

backend/tests/test_sitemap.py

@@ -42,3 +42,53 @@ def test_every_loc_uses_the_www_host(sitemap):
     # The apex 301s to www. A <loc> that redirects burns a crawl per URL.
     assert "https://www.schoolcompare.co.uk" in sitemap
     assert "https://schoolcompare.co.uk" not in sitemap
+
+
+def test_school_with_results_is_listed(sitemap):
+    assert "/school/100001-alpha-primary" in sitemap
+
+
+def test_school_with_no_results_and_no_ofsted_is_omitted(sitemap):
+    # Nothing for a search result to say about it. Submitting it spends crawl
+    # budget and drags the corpus-wide quality signal down.
+    assert "/school/100002" not in sitemap
+
+
+def test_no_invented_priority_or_changefreq(sitemap):
+    # Google ignores both. They were noise dressed as signal.
+    assert "<priority>" not in sitemap
+    assert "<changefreq>" not in sitemap
+
+
+def test_ofsted_date_becomes_lastmod(monkeypatch):
+    from backend import app as app_module
+    import datetime
+
+    def _df():
+        base = _schools_df()
+        base.loc[base["urn"] == 100001, "ofsted_date"] = datetime.date(2024, 3, 14)
+        return base
+
+    monkeypatch.setattr(app_module, "load_school_data", _df)
+    xml = app_module.build_sitemap()
+    assert "<lastmod>2024-03-14</lastmod>" in xml
+
+
+def test_no_lastmod_invented_when_date_unknown(monkeypatch):
+    # An always-now lastmod is a claim Google learns to distrust. Absent
+    # honestly means unknown.
+    from backend import app as app_module
+
+    def _df():
+        df = _schools_df()
+        df["ofsted_date"] = None
+        return df
+
+    monkeypatch.setattr(app_module, "load_school_data", _df)
+    xml = app_module.build_sitemap()
+    assert "<lastmod>" not in xml
+
+
+def test_static_routes_are_listed(sitemap):
+    for path in ("/", "/rankings", "/compare", "/admissions"):
+        assert f"<loc>https://www.schoolcompare.co.uk{path}</loc>" in sitemap