fix(rectification): keep opening greeting across set-focus

set-focus only attaches the question stem. Retracting live Chinese before
it wiped the opening hello with an empty replace. Other public tools still
retract planning prose.

BUG-533.

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

frontend/src/lib/rectification-agentic/v9/step-answer.ts

@@ -6,7 +6,8 @@
  * Once the current step looks like the spoken reply — Chinese sentence end,
  * or live-unlock after compare/offer/result tools — tokens may stream as
  * `live`. A later public tool-call retracts that speculative stream so
- * "Let me set" never stays in `answer.delta`.
+ * "Let me set" never stays in `answer.delta`. Exception: `rectification-set-focus`
+ * only attaches the question stem; live greeting/handoff in the same step stays.
  */
 
 export type StepAnswerChunk = Readonly<{
@@ -45,6 +46,11 @@ const SPOKEN_LIVE_UNLOCK_TOOLS = new Set([
   "rectification-read-diagnostics",
 ]);
 
+/** set-focus writes the stem onto the same turn; it is not planning prose. */
+const KEEP_LIVE_SPOKEN_TOOLS = new Set([
+  "rectification-set-focus",
+]);
+
 function resetBuffers(state: StepAnswerState): void {
   state.text = "";
   state.pieces = [];
@@ -153,14 +159,19 @@ export function applyStepAnswerChunk(
     }
     case "tool-call":
       if (isPublicToolCall(chunk, isPublicTool)) {
-        const retracted = retractLive(state);
         state.calledTool = true;
+        if (KEEP_LIVE_SPOKEN_TOOLS.has(toolName(chunk))) return { kind: "none" };
+        const retracted = retractLive(state);
         return retracted.kind === "retract" ? retracted : { kind: "none" };
       }
       return { kind: "none" };
     case "tool-result":
     case "tool-error": {
       if (isPublicToolCall(chunk, isPublicTool)) state.calledTool = true;
+      if (KEEP_LIVE_SPOKEN_TOOLS.has(toolName(chunk))) {
+        resetBuffers(state);
+        return { kind: "none" };
+      }
       const discarded = state.calledTool || state.text.length > 0;
       const retracted = retractLive(state);
       resetBuffers(state);