fix(web): keep rectification emit types compatible with next build

The spoken/thinking splitter must accept sync or async emit, matching the runner input type.

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

frontend/src/lib/rectification-agentic/v9/agent-run.ts

@@ -843,7 +843,7 @@ async function publishSplitSpokenAndThinking(
   publishedSpoken: string,
   answerText: string,
   publish: (event: PublicStreamEvent) => Promise<void>,
-  emit: (event: PublicStreamEvent) => Promise<void>,
+  emit: (event: PublicStreamEvent) => Promise<void> | void,
   finalize = false,
 ): Promise<{ thinking: string; spoken: string; spokenDelta: string }> {
   const split = finalize

frontend/tests/rectification-agentic-entry.test.ts

@@ -237,6 +237,8 @@ test("usage completes or releases without hiding settlement failures", () => {
   assert.match(run, /thinking: "disabled"/);
   assert.match(run, /toPublicThinkingDelta/);
   assert.match(run, /splitRectificationSpokenAndThinking/);
+  assert.match(run, /emit\(event: PublicStreamEvent\): Promise<void> \| void;/);
+  assert.match(run, /emit: \(event: PublicStreamEvent\) => Promise<void> \| void,/);
   assert.match(route, /featureKey: "rectification"/);
   assert.match(route, /rectification:case:\$\{caseId\}/);
 });