Add support for Datadog backend

[nirga]

Description

Add support for Datadog as an observability backend, enabling users to query OpenTelemetry traces from Datadog APM.

Motivation

Datadog is one of the most popular observability platforms with extensive APM and tracing capabilities. Adding Datadog backend support would enable a large user base to leverage this MCP server for AI-powered trace analysis and debugging of their LLM applications.

Implementation Requirements

1. Backend Implementation

• Create src/openllmetry_mcp/backends/datadog.py following the abstract interface in backends/base.py
• Implement the following methods:
  • search_traces() - Query traces using Datadog Trace API
  • get_trace() - Retrieve full trace details
  • list_services() - List available services
  • get_aggregated_usage() - Aggregate token usage metrics

2. Configuration

• Add datadog as a backend type option
• Required configuration:
  • BACKEND_URL: Datadog site URL (e.g., https://api.datadoghq.com or https://api.datadoghq.eu)
  • BACKEND_API_KEY: Datadog API key
  • BACKEND_APP_KEY: Datadog Application key (required for trace queries)
• Update .env.example with Datadog configuration example

3. API Integration

Reference Datadog APIs:

• Trace Search API
• APM API
• Authentication: DD-API-KEY and DD-APPLICATION-KEY headers

4. OpenLLMetry Support

Ensure proper parsing of OpenLLMetry semantic conventions (gen_ai.* attributes) from Datadog trace spans.

5. Documentation

• Add Datadog backend configuration to README.md
• Include Claude Desktop integration example
• Document both US and EU site configurations
• Add troubleshooting section for common Datadog connection issues

6. Testing

• Add unit tests in tests/backends/test_datadog.py
• Test trace querying with Datadog's query syntax
• Test filtering, aggregation, and pagination
• Test error handling and authentication

Example Configuration

BACKEND_TYPE=datadog
BACKEND_URL=https://api.datadoghq.com
BACKEND_API_KEY=dd_api_key_here
BACKEND_APP_KEY=dd_app_key_here

References

• Datadog OpenTelemetry Integration
• Datadog Trace Search
• Existing backend implementations: backends/jaeger.py, backends/tempo.py, backends/traceloop.py

Acceptance Criteria

• Datadog backend implementation complete
• All abstract methods implemented
• Configuration documented (US and EU sites)
• Tests passing
• README updated with Datadog examples
• Works with Claude Desktop integration