Add session-relative elapsed time to context for realistic time awareness

Currently only the date is injected into Claude's context. Claude has no sense of how much time has passed within a session or between messages.

Request

Inject a session-relative elapsed timestamp (e.g. T0.00 at session start, T1.15 after 1h15m) alongside the existing date injection.

Why it matters

• Claude currently estimates task durations using human developer timelines ("this will take 12 weeks") when the actual Claude-time might be 15 sessions across 3 days
• No way to distinguish "user was away for 2 hours" from "user is actively waiting" — affects pacing and response style
• /insights reports inflate usage time (e.g. "750 hours") because they measure session wall-clock time with no way to distinguish active work from an idle terminal left open overnight
• Session-relative format avoids privacy concerns (no real-world clock or timezone leaked) while giving Claude meaningful time context