feat(api): implement OpenAPI/REST API for file conversions

- Add comprehensive REST API at /api/v1 with modular structure
- Implement authentication endpoints (register, login, logout, me)
- Add converter listing and format discovery endpoints
- Create job management and file download endpoints
- Add health check endpoint for monitoring
- Set up CORS support for browser-based API clients
- Create API middleware for JWT authentication
- Add environment variables for API configuration
- Include comprehensive API documentation and test script

Infrastructure:
- Enhanced CI/CD workflow for custom Docker registries
- Docker Compose setup with dev, prod, and monitoring profiles
- Claude.ai integration files for development workflow
- Environment-based configuration with .env.development

Known limitations:
- JWT authentication context needs fixing (using ALLOW_UNAUTHENTICATED=true)
- Swagger UI temporarily disabled due to composition error
- File upload endpoint needs multipart/form-data support

The API code is isolated in src/api/ directory to maintain separation
from the existing codebase, making it easy to maintain or contribute back.

.claude/test.md

@@ -0,0 +1,45 @@
+# Run Tests and Checks
+
+Please run the following tests and checks for the ConvertX project:
+
+1. **Type Checking**:
+   ```bash
+   bun run typecheck
+   ```
+   Fix any TypeScript errors found
+
+2. **Linting**:
+   ```bash
+   bun run lint
+   ```
+   Fix any linting issues
+
+3. **Unit Tests** (if available):
+   ```bash
+   bun test
+   ```
+
+4. **Build Check**:
+   ```bash
+   bun run build
+   ```
+   Ensure the build completes successfully
+
+5. **API Tests** (when implemented):
+   - Test authentication endpoints
+   - Test file upload endpoints
+   - Test conversion endpoints
+   - Test error handling
+
+6. **Docker Build Test**:
+   ```bash
+   docker build -t convertx-test .
+   ```
+
+7. **Integration Test** (if safe to run):
+   - Start the application
+   - Upload a test file
+   - Convert it
+   - Verify the output
+
+Please run these checks and report any issues found. If there are failures, analyze and suggest fixes.