feat: upgrade NestJS to v11 and migrate to ESLint flat config (#10746)
### Description
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This PR upgrades the NestJS example from v10 to v11 and modernizes the
project configuration. The main changes include:
- **NestJS Upgrade**: Upgrade `@nestjs/common`, `@nestjs/core`, and
`@nestjs/platform-express` from v10 to v11
- **ESLint Migration**: Migrate from legacy `.eslintrc.js` format to
modern flat config format using `eslint.config.mjs`
- **Configuration Cleanup**: Remove legacy configuration files
(`.eslintrc.js`, `.prettierrc.js`) and replace with modern equivalents
- **Package Updates**: Update dependencies and scripts across all
packages in the monorepo
- **Project Structure**: Modernize the overall project structure with
updated TypeScript and build configurations
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## Testing Instructions
1. **Install Dependencies**
```bash
pnpm install
pnpm build
```
2. **Verify NestJS API**
```bash
pnpm --filter=api run dev
```
- Check that the API starts without errors
- Verify endpoints are accessible at `http://localhost:3000`
3. **Test Web Application**
```bash
pnpm --filter=web run dev
```
- Ensure the web app runs on `http://localhost:3001`
- Verify the UI displays correctly
4. **Linting and Formatting**
```bash
pnpm run lint
pnpm run format
```
- Confirm ESLint runs without errors
- Verify Prettier formatting works correctly
5. **Build Process**
```bash
pnpm build
```
- Ensure all packages build successfully
- Check for any TypeScript compilation errors
6. **Run Tests**
```bash
pnpm test
```
- Verify all tests pass
- Check that Jest configuration works properly