Add structured logging via @azure/logger

[daviburg]

Context

The Node SDK has zero logging throughout its infrastructure layer — ConnectorHttpClient, ConnectorClientBase, and all generated clients are completely silent. The .NET SDK logs via the Azure.Core pipeline automatically at Info (request start), Info (response received), and Warning (retry attempts).

Proposed change

Add @azure/logger with the azure:connectors: prefix namespace:

import { createClientLogger } from "@azure/logger";

const logger = createClientLogger("connectors");

// In ConnectorHttpClient.sendAsync():
logger.info(`→ ${method} ${url}`);
// On response:
logger.info(`← ${response.status} ${method} ${url} (${elapsed}ms)`);
// On retry:
logger.warning(`Retry ${attempt}/${maxRetries} for ${method} ${url} after ${delay}ms`);
// On error:
logger.error(`${method} ${url} failed: ${error.message}`);

Consumers opt in to log output by setting:

AZURE_LOG_LEVEL=info   # or verbose, warning, error

This is a non-breaking additive change and can be shipped independently of the other infrastructure issues.

Azure SDK guideline

• DO use @azure/logger
• Namespace format: azure:<service> (e.g., azure:connectors)