[FEATURE] Add tool_parameters to OTEL telemetry for Skill tool invocations

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When using OpenTelemetry telemetry to monitor Claude Code usage, the tool_result events include tool_parameters for the Bash tool, but this field is empty for Skill tool invocations. This makes it impossible to track which skills are being used via native telemetry. Organizations want to understand skill adoption across their teams to make data-driven decisions about training and skill development.

Proposed Solution

When the Skill tool is invoked, populate the tool_parameters field in tool_result events with the skill name and arguments:
{
"event.name": "tool_result",
"tool_name": "Skill",
"tool_parameters": "{\"skill\":\"codegen\",\"args\":\"\"}",
"success": "true"
}

This matches the existing pattern for Bash tool where tool_parameters includes command details.

Alternative Solutions

Currently the only workaround is implementing a PostToolUse hook that manually extracts the skill name from tool_input and sends a custom metric. This adds complexity and doesn't benefit from native telemetry's robustness and consistency.

Priority

Low - Nice to have

Feature Category

Configuration and settings

Use Case Example

1. Organization deploys Claude Code to 50+ engineers with OTEL telemetry enabled
2. Admin creates Datadog dashboard to track tool usage patterns
3. Admin wants to see which skills (codegen, commit, pr) are most used
4. Currently: tool_result events show tool_name:"Skill" but no skill name
5. With this feature: Could query tool_parameters.skill to see "codegen" used 500 times, "commit" 200 times
6. This helps prioritize which skills to improve or create custom skills for common workflows

Additional Context

_No response_