fix(web): isolate rectification answers from tool-step planning text

Mastra intermediate text-delta was published as answer.delta, then set-focus domain errors reset the attempt and replayed evidence. Publish only the terminal no-tool step, persist the next probe on the server, and ground batch quotes in the source turn.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/tests/rectification-v9-migration.test.ts

@@ -1253,3 +1253,21 @@ test("PR-4 exposes only the explicit V2 service-role RPC signatures", () => {
     /grant execute on function public\.confirm_agentic_rectification_candidate_for_case_v2\(uuid, uuid, uuid, uuid, uuid, text, uuid\)\s+to service_role/,
   );
 });
+
+test("turn origin migration stays out of the identity foundation", () => {
+  const turnOriginMigration = readFileSync(
+    new URL("../supabase/migrations/20260824030000_rectification_turn_origin.sql", import.meta.url),
+    "utf8",
+  );
+  const turnOriginDbCopy = fileURLToPath(
+    new URL("../db/migrations/20260824030000_rectification_turn_origin.sql", import.meta.url),
+  );
+  assert.equal(
+    existsSync(turnOriginDbCopy),
+    false,
+    "business migration must not be copied into frontend/db/migrations (BUG-127/BUG-144)",
+  );
+  assert.match(turnOriginMigration, /record_agentic_rectification_turn_origin/);
+  assert.match(turnOriginMigration, /message_origin/);
+  assert.match(turnOriginMigration, /suggestion_click/);
+});