Add OpenTelemetry environment variable support

[ivancasco]

Pass OTEL configuration environment variables through to Claude Code to enable observability and tracing.

Supported OTEL env vars from Claude Code documentation:

• CLAUDE_CODE_ENABLE_TELEMETRY (required to enable telemetry)
• OTEL_METRICS_EXPORTER
• OTEL_EXPORTER_OTLP_PROTOCOL
• OTEL_EXPORTER_OTLP_ENDPOINT
• OTEL_EXPORTER_OTLP_HEADERS
• OTEL_EXPORTER_OTLP_METRICS_CLIENT_KEY
• OTEL_EXPORTER_OTLP_METRICS_CLIENT_CERTIFICATE
• OTEL_METRIC_EXPORT_INTERVAL
• OTEL_METRICS_INCLUDE_SESSION_ID
• OTEL_METRICS_INCLUDE_VERSION
• OTEL_METRICS_INCLUDE_ACCOUNT_UUID

🤖 Generated with Claude Code

[sid374]

We should lean on the settings.json files (docs here: https://docs.anthropic.com/en/docs/claude-code/settings) to set up these env variables instead of defining them explicitly in the action.

The env vars you have listed here are only a small subset of the supported OTEL env vars, and we'd end up writing more config here every time we discover a new one that's useful. Instead the flow should be:

1. Create a .claude/settings.json in your repo and check it in or create it as a separate workflow step before calling the claude action if you'd like to use Secrets
2. Add this to your settings.json + any additional OTEL env vars

  "env": {
    "CLAUDE_CODE_ENABLE_TELEMETRY": "1",
    "OTEL_METRICS_EXPORTER": "otlp"
  }

3. Continue...

We will also update our docs to reflect this.