feat(api): name each school's type group, and send search its nursery provision

The school page and the search rows now print a school's type in the search
filter's terms ("State school", "Independent school") instead of GIAS's 34
establishment types. The list, place and detail payloads carry type_group,
computed with the filter's own type_group_for, so the two never disagree; a
type in no group stays null and the page prints the register's name.

Search rows flag a nursery class, so nursery_provision joins SCHOOL_COLUMNS.

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

backend/app.py

@@ -634,6 +634,18 @@ def _with_whole_school_pupils(rows: pd.DataFrame, source: pd.DataFrame) -> pd.Da
     return rows.assign(total_pupils=whole)
 
 
+def _with_type_group(rows: pd.DataFrame) -> pd.DataFrame:
+    """Name each row's search-filter type group, or None for a type in no group.
+
+    The school page and the search rows print it ("State school") in place of
+    the GIAS establishment type, and an independent school gets a Fee-paying
+    flag from it.
+    """
+    if "school_type" not in rows.columns:
+        return rows
+    return rows.assign(type_group=rows["school_type"].map(type_group_for))
+
+
 # Input validation helpers
 def _names_in_group(names: pd.Series, in_group) -> set:
     """The distinct names in a column that a group predicate accepts.
@@ -965,7 +977,7 @@ async def get_schools(
     total = len(schools_df)
     start_idx = (page - 1) * page_size
     end_idx = start_idx + page_size
-    schools_df = schools_df.iloc[start_idx:end_idx]
+    schools_df = _with_type_group(schools_df.iloc[start_idx:end_idx])
 
     return {
         "schools": clean_for_json(schools_df),
@@ -1029,6 +1041,7 @@ async def get_school_details(request: Request, urn: int):
             "school_name": latest.get("school_name", ""),
             "local_authority": latest.get("local_authority", ""),
             "school_type": latest.get("school_type", ""),
+            "type_group": type_group_for(latest.get("school_type")),
             "address": latest.get("address", ""),
             "religious_denomination": latest.get("religious_denomination", ""),
             "age_range": latest.get("age_range", ""),
@@ -1522,13 +1535,12 @@ async def get_place(request: Request, kind: str, slug: str,
     # warning. Ordered de-duplication keeps the column order and the warning
     # cannot come back.
     #
-    # nursery_provision and parliamentary_constituency are not in
-    # SCHOOL_COLUMNS and the place table shows both. The `in rows.columns`
-    # guard is what keeps a mart the pipeline has not rebuilt working: those
-    # two are the optional GIAS columns data_loader degrades to NULL.
+    # parliamentary_constituency is not in SCHOOL_COLUMNS and the place table
+    # shows it. The `in rows.columns` guard is what keeps a mart the pipeline
+    # has not rebuilt working: it and nursery_provision are the optional GIAS
+    # columns data_loader degrades to NULL.
     cols = [c for c in dict.fromkeys(
                 SCHOOL_COLUMNS + ["latitude", "longitude", "phase",
-                                  "nursery_provision",
                                   "parliamentary_constituency",
                                   "rwm_expected_pct", "attainment_8_score",
                                   "total_pupils"])
@@ -1558,7 +1570,8 @@ async def get_place(request: Request, kind: str, slug: str,
                   # variants that exist rather than 404s.
                   "phases": [ph for ph in ("primary", "secondary")
                              if place.publishes_phase(ph)]},
-        "schools": clean_for_json(_with_whole_school_pupils(rows[cols], rows)),
+        "schools": clean_for_json(
+            _with_type_group(_with_whole_school_pupils(rows[cols], rows))),
         "averages": averages,
     }