feat(site_domain): restore access_key enforcement for FQDN lookups

- api_crud_v3: strip falsy access_key values; restrict keyless queries
  to public domains (both site_access_key and site_domain_access_key
  must be NULL/empty); 75-line recursive block replaced with ~16 lines
- lib_sql_search: expand virtual 'access_key' field into priority SQL —
  site_access_key first, site_domain_access_key as fallback
- cms.py: add site_domain_access_key to site_domain searchable_fields
- docs: update frontend guide with access key behavior and examples
- e2e test: expand to cover all valid/invalid access key scenarios (15/15)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/lib_sql_search.py

@@ -199,7 +199,11 @@ def sql_search_qry_part(
                     if hasattr(item, 'field'):
                         clause, item_data = process_filter(item)
                         node_clauses.append(clause); data.update(item_data)
-                    else: node_clauses.append(f"({process_node(item, current_depth + 1)})")
+                    else:
+                        # Recurse into nested SearchQuery; only append if non-empty
+                        sub_clause = process_node(item, current_depth + 1)
+                        if sub_clause:
+                            node_clauses.append(f"({sub_clause})")
                 if node_clauses:
                     joiner = ' AND ' if 'and' in filter_attr else ' OR '
                     clauses.append(f"({joiner.join(node_clauses)})")
@@ -261,6 +265,18 @@ def sql_search_qry_part(
                     except Exception as e:
                         log.warning(f"Failed to resolve random ID for field {target_field}: {e}")
 
+        # site_domain: 'access_key' is a virtual field.
+        # site_access_key (site-level) takes priority; fall back to site_domain_access_key
+        # when site_access_key is not set (NULL or empty).
+        if target_field == 'access_key' and table_name and 'site_domain' in table_name:
+            sql_op = operator_map.get(f.op.lower())
+            if not sql_op: raise HTTPException(status_code=400, detail=f"Unsupported operator: {f.op}")
+            p1, p2 = get_param_name(), get_param_name()
+            return (
+                f"(site_access_key {sql_op} :{p1} OR "
+                f"((site_access_key IS NULL OR site_access_key = '') AND site_domain_access_key {sql_op} :{p2}))"
+            ), {p1: f.value, p2: f.value}
+
         if searchable_fields is not None and target_field not in searchable_fields:
             # Fallback check for original field just in case
             if f.field not in searchable_fields: