feat(next-app-router-4000,next-app-router-4001): add Cypress e2e test configuration

- Add Cypress config files for next-app-router-4000 and next-app-router-4001
- Create test directory structure with support files and fixtures
- Add basic e2e tests for both apps
- Configure proper TypeScript settings for Cypress

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: ScriptedAlchemy

apps/next-app-router/next-app-router-4000/cypress.config.ts

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+import { nxE2EPreset } from '@nx/cypress/plugins/cypress-preset';
+import { defineConfig } from 'cypress';
+
+export default defineConfig({
+  projectId: '27e40c91-5ac3-4433-8a87-651d10f51cf6',
+  e2e: {
+    ...nxE2EPreset(__filename, { cypressDir: 'cypress' }),
+    baseUrl: 'http://localhost:4000',
+  },
+  defaultCommandTimeout: 20000,
+  retries: {
+    runMode: 2,
+    openMode: 1,
+  },
+});

apps/next-app-router/next-app-router-4000/cypress/e2e/app.cy.ts

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+import { getH1 } from '../support/app.po';
+
+describe('next-app-router-4000', () => {
+  beforeEach(() => cy.visit('/'));
+
+  describe('Home page', () => {
+    it('should display examples heading', () => {
+      getH1().contains('Examples');
+    });
+
+    it('should have remote button from module federation', () => {
+      cy.get('button').contains('Button from remote').should('exist');
+    });
+
+    it('should have navigation links', () => {
+      cy.get('a[href="/layouts"]').should('exist');
+      cy.get('a[href="/error-handling"]').should('exist');
+      cy.get('a[href="/loading"]').should('exist');
+    });
+  });
+
+  describe('Navigation', () => {
+    it('should navigate to layouts page', () => {
+      cy.get('a[href="/layouts"]').first().click();
+      cy.url().should('include', '/layouts');
+    });
+
+    it('should navigate to parallel routes', () => {
+      cy.get('a[href="/parallel-routes"]').first().click();
+      cy.url().should('include', '/parallel-routes');
+    });
+  });
+
+  describe('Module Federation', () => {
+    it('should load remote button component', () => {
+      cy.get('button').contains('Button from remote').should('be.visible');
+    });
+  });
+});

apps/next-app-router/next-app-router-4000/cypress/fixtures/example.json

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+{
+  "name": "Using fixtures to represent data",
+  "email": "hello@cypress.io",
+  "body": "Fixtures are a great way to mock data for responses to routes"
+}

apps/next-app-router/next-app-router-4000/cypress/support/app.po.ts

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+export const getH1 = () => cy.get('h1');
+export const getH2 = () => cy.get('h2');
+export const getH3 = () => cy.get('h3');

apps/next-app-router/next-app-router-4000/cypress/support/commands.ts

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+// ***********************************************
+// This example commands.ts shows you how to
+// create various custom commands and overwrite
+// existing commands.
+//
+// For more comprehensive examples of custom
+// commands please read more here:
+// https://on.cypress.io/custom-commands
+// ***********************************************

apps/next-app-router/next-app-router-4000/cypress/support/e2e.ts

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+// ***********************************************************
+// This example support/e2e.ts is processed and
+// loaded automatically before your test files.
+//
+// This is a great place to put global configuration and
+// behavior that modifies Cypress.
+//
+// You can change the location of this file or turn off
+// automatically serving support files with the
+// 'supportFile' configuration option.
+//
+// You can read more here:
+// https://on.cypress.io/configuration
+// ***********************************************************
+
+// Import commands.js using ES2015 syntax:
+import './commands';

apps/next-app-router/next-app-router-4000/cypress/tsconfig.json

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+{
+  "extends": "../tsconfig.json",
+  "compilerOptions": {
+    "sourceMap": false,
+    "outDir": "../../../dist/out-tsc",
+    "allowJs": true,
+    "types": ["cypress", "node"],
+    "esModuleInterop": true,
+    "forceConsistentCasingInFileNames": true,
+    "strict": true,
+    "skipLibCheck": true
+  },
+  "include": ["**/*.ts", "**/*.js", "../cypress.config.ts"]
+}

apps/next-app-router/next-app-router-4001/cypress.config.ts

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+import { nxE2EPreset } from '@nx/cypress/plugins/cypress-preset';
+import { defineConfig } from 'cypress';
+
+export default defineConfig({
+  projectId: '27e40c91-5ac3-4433-8a87-651d10f51cf6',
+  e2e: {
+    ...nxE2EPreset(__filename, { cypressDir: 'cypress' }),
+    baseUrl: 'http://localhost:4001',
+  },
+  defaultCommandTimeout: 20000,
+  retries: {
+    runMode: 2,
+    openMode: 1,
+  },
+});

apps/next-app-router/next-app-router-4001/cypress/e2e/app.cy.ts

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+describe('next-app-router-4001', () => {
+  beforeEach(() => cy.visit('/'));
+
+  describe('Remote component (Button)', () => {
+    it('should export Button component for module federation', () => {
+      // This app serves as a remote that exports the Button component
+      // Testing that the app loads successfully
+      cy.visit('/');
+    });
+  });
+
+  describe('Button component functionality', () => {
+    it('should render default button', () => {
+      // If there's a test page that renders the button
+      cy.visit('/');
+      // Check if the page loads without errors
+      cy.get('body').should('exist');
+    });
+  });
+
+  describe('Module Federation Remote', () => {
+    it('should be accessible as a remote module', () => {
+      // Verify the app is running and accessible
+      cy.request('/').its('status').should('eq', 200);
+    });
+  });
+});

apps/next-app-router/next-app-router-4001/cypress/fixtures/example.json

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+{
+  "name": "Using fixtures to represent data",
+  "email": "hello@cypress.io",
+  "body": "Fixtures are a great way to mock data for responses to routes"
+}