Fixes issue #726 by adding config to configToSave object (#728)

The saveConfig() function only includes a hardcoded subset of properties
when writing the config file. Any property not explicitly listed (like
disableResponseStorage) will be dropped.
I have added `disableResponseStorage` to the `configToSave` object as
the immediate fix.

[Linking Issue this fixes.](https://github.com/openai/codex/issues/726)

codex-cli/tests/disableResponseStorage.agentLoop.test.ts

@@ -0,0 +1,93 @@
+/**
+ * codex-cli/tests/disableResponseStorage.agentLoop.test.ts
+ *
+ * Verifies AgentLoop's request-building logic for both values of
+ * disableResponseStorage.
+ */
+
+import { describe, it, expect, vi } from "vitest";
+import { AgentLoop } from "../src/utils/agent/agent-loop";
+import type { AppConfig } from "../src/utils/config";
+import { ReviewDecision } from "../src/utils/agent/review";
+
+/* ─────────── 1.  Spy + module mock ─────────────────────────────── */
+const createSpy = vi.fn().mockResolvedValue({
+  data: { id: "resp_123", status: "completed", output: [] },
+});
+
+vi.mock("openai", () => ({
+  default: class {
+    public responses = { create: createSpy };
+  },
+  APIConnectionTimeoutError: class extends Error {},
+}));
+
+/* ─────────── 2.  Parametrised tests ─────────────────────────────── */
+describe.each([
+  { flag: true, title: "omits previous_response_id & sets store:false" },
+  { flag: false, title: "sends previous_response_id & allows store:true" },
+])("AgentLoop with disableResponseStorage=%s", ({ flag, title }) => {
+  /* build a fresh config for each case */
+  const cfg: AppConfig = {
+    model: "o4-mini",
+    provider: "openai",
+    instructions: "",
+    disableResponseStorage: flag,
+    notify: false,
+  };
+
+  it(title, async () => {
+    /* reset spy per iteration */
+    createSpy.mockClear();
+
+    const loop = new AgentLoop({
+      model: cfg.model,
+      provider: cfg.provider,
+      config: cfg,
+      instructions: "",
+      approvalPolicy: "suggest",
+      disableResponseStorage: flag,
+      additionalWritableRoots: [],
+      onItem() {},
+      onLoading() {},
+      getCommandConfirmation: async () => ({ review: ReviewDecision.YES }),
+      onLastResponseId() {},
+    });
+
+    await loop.run([
+      {
+        type: "message",
+        role: "user",
+        content: [{ type: "input_text", text: "hello" }],
+      },
+    ]);
+
+    expect(createSpy).toHaveBeenCalledTimes(1);
+
+    const call = createSpy.mock.calls[0];
+    if (!call) {
+      throw new Error("Expected createSpy to have been called at least once");
+    }
+    const payload: any = call[0];
+
+    if (flag) {
+      /* behaviour when ZDR is *on* */
+      expect(payload).not.toHaveProperty("previous_response_id");
+      if (payload.input) {
+        payload.input.forEach((m: any) => {
+          expect(m.store === undefined ? false : m.store).toBe(false);
+        });
+      }
+    } else {
+      /* behaviour when ZDR is *off* */
+      expect(payload).toHaveProperty("previous_response_id");
+      if (payload.input) {
+        payload.input.forEach((m: any) => {
+          if ("store" in m) {
+            expect(m.store).not.toBe(false);
+          }
+        });
+      }
+    }
+  });
+});