test: add integration test to verify stdout/stderr routing (#17280)

Co-authored-by: Allen Hutchison <adh@google.com>

integration-tests/stdout-stderr-output-error.responses

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+{"method":"generateContentStream","response":[{"candidates":[{"content":{"parts":[{"text":"I could not find the file `nonexistent-file-that-does-not-exist.txt` in the current directory or its subdirectories. Please verify the file path or name."}],"role":"model"},"finishReason":"STOP","index":0}],"usageMetadata":{"promptTokenCount":10,"candidatesTokenCount":25,"totalTokenCount":35,"promptTokensDetails":[{"modality":"TEXT","tokenCount":10}]}}]}

integration-tests/stdout-stderr-output.responses

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+{"method":"generateContentStream","response":[{"candidates":[{"content":{"parts":[{"text":"Hello! How can I help you today?"}],"role":"model"},"finishReason":"STOP","index":0}],"usageMetadata":{"promptTokenCount":5,"candidatesTokenCount":9,"totalTokenCount":14,"promptTokensDetails":[{"modality":"TEXT","tokenCount":5}]}}]}

integration-tests/stdout-stderr-output.test.ts

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+/**
+ * @license
+ * Copyright 2025 Google LLC
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+import { describe, it, expect, beforeEach, afterEach } from 'vitest';
+import { join } from 'node:path';
+import { TestRig } from './test-helper.js';
+
+describe('stdout-stderr-output', () => {
+  let rig: TestRig;
+
+  beforeEach(() => {
+    rig = new TestRig();
+  });
+
+  afterEach(async () => {
+    await rig.cleanup();
+  });
+
+  it('should send model response to stdout and app messages to stderr', async ({
+    signal,
+  }) => {
+    await rig.setup('prompt-output-test', {
+      fakeResponsesPath: join(
+        import.meta.dirname,
+        'stdout-stderr-output.responses',
+      ),
+    });
+
+    const { stdout, exitCode } = await rig.runWithStreams(['-p', 'Say hello'], {
+      signal,
+    });
+
+    expect(exitCode).toBe(0);
+    expect(stdout.toLowerCase()).toContain('hello');
+    expect(stdout).not.toMatch(/^\[ERROR\]/m);
+    expect(stdout).not.toMatch(/^\[INFO\]/m);
+  });
+
+  it('should handle missing file with message to stdout and error to stderr', async ({
+    signal,
+  }) => {
+    await rig.setup('error-output-test', {
+      fakeResponsesPath: join(
+        import.meta.dirname,
+        'stdout-stderr-output-error.responses',
+      ),
+    });
+
+    const { stdout, exitCode } = await rig.runWithStreams(
+      ['-p', '@nonexistent-file-that-does-not-exist.txt explain this'],
+      { signal },
+    );
+
+    expect(exitCode).toBe(0);
+    expect(stdout.toLowerCase()).toMatch(
+      /could not find|not exist|does not exist/,
+    );
+  });
+});