fix(prompt): treat post-dispatch failures as accepted

src/features/background-agent/session-route.test.ts

@@ -41,6 +41,33 @@ describe("background-agent session routing", () => {
     expect(promptAsync.mock.calls[0]?.[0].query).toEqual({ directory: "/workspace/project" })
   })
 
+  test("#given routed promptAsync reports ambiguous EOF after dispatch #when the background route handles it #then it treats the prompt as accepted", async () => {
+    // given
+    const promptAsync = mock(async () => {
+      throw new Error("JSON Parse error: Unexpected EOF")
+    })
+    const client = {
+      session: {
+        promptAsync,
+      },
+    }
+    const args = {
+      path: { id: "ses_background_route_ambiguous_eof" },
+      body: { parts: [{ type: "text", text: "continue" }] },
+    }
+
+    // when
+    const result = await promptAsyncInDirectory(
+      unsafeTestValue(client),
+      unsafeTestValue(args),
+      "/workspace/project",
+    )
+
+    // then
+    expect(result).toBeUndefined()
+    expect(promptAsync).toHaveBeenCalledTimes(1)
+  })
+
   test("#given a background retry prompt just dispatched #when the same child session is prompted again immediately #then retry routing defers instead of enqueueing", async () => {
     // given
     const promptAsync = mock(async () => undefined)