fix(agents): address review feedback on #61481 phase-integrity hardening

src/agents/pi-embedded-subscribe.handlers.messages.ts

@@ -313,13 +313,15 @@ export function handleMessageUpdate(
   }
   const next =
     phaseAwareVisibleText ||
-    ctx
-      .stripBlockTags(ctx.state.deltaBuffer, {
-        thinking: false,
-        final: false,
-        inlineCode: createInlineCodeState(),
-      })
-      .trim();
+    (deliveryPhase === "final_answer"
+      ? ""
+      : ctx
+          .stripBlockTags(ctx.state.deltaBuffer, {
+            thinking: false,
+            final: false,
+            inlineCode: createInlineCodeState(),
+          })
+          .trim());
   if (next) {
     const wasThinking = ctx.state.partialBlockState.thinking;
     const visibleDelta = chunk ? ctx.stripBlockTags(chunk, ctx.state.partialBlockState) : "";

src/gateway/sessions-history-http.test.ts

@@ -363,7 +363,8 @@ describe("session history HTTP endpoints", () => {
 
       const visible = await appendAssistantMessageToSessionTranscript({
         sessionKey: "agent:main:main",
-        text: JSON.stringify({
+        text: "Done.",
+        message: {
           role: "assistant",
           content: [
             {
@@ -377,7 +378,7 @@ describe("session history HTTP endpoints", () => {
               textSignature: JSON.stringify({ v: 1, id: "item_final", phase: "final_answer" }),
             },
           ],
-        }),
+        },
         storePath,
       });
       expect(visible.ok).toBe(true);