Feature request: expose session start timestamp for AI efficiency monitoring

Feature Request

Summary: Expose the session start timestamp so users can track how long a Claude Code session has been running.

Motivation: When asking Claude Code about session metadata (e.g., "what time did I start this session?"), it cannot answer because session start time is not available in context. This makes it difficult to:

• Monitor AI efficiency (e.g., how long a task took end-to-end)
• Understand the cost of a session in terms of wall-clock time
• Track productivity improvements when adopting AI-assisted workflows

Proposed change: Surface the session start timestamp (and optionally elapsed time) as part of the context Claude Code has access to, similar to how currentDate is already injected. Even a read-only system variable like session_started_at would be sufficient.

Use case example: A data engineer wants to log that a complex SQL refactor + PR creation workflow took 45 minutes with AI assistance vs. several hours manually. Without a session start time, this measurement isn't possible from within the session.