[FEATURE] Show conversation duration / elapsed time

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 working on longer conversations or tasks in Claude Code, I have no way
to know how much time has elapsed in the current session. This makes it
difficult to track time spent on a task — for personal productivity,
client billing, or general awareness.

Proposed Solution

Show elapsed time for the current conversation somewhere in the Claude Code UI —
for example in the status bar or conversation header. Ideally a simple timer
that starts when the conversation begins and shows hours:minutes.

Alternative Solutions

Currently I manually check the clock before and after a session, which is
error-prone and easy to forget. There is no built-in workaround.

Alternative proposed solution: show time next to the message when I sent it.

Priority

Medium - Would be very helpful

Feature Category

Other

Use Case Example

1. I start a Claude Code session to work on a feature
2. I get into the flow and lose track of time
3. At some point I want to know how long I've been working
4. With this feature I could glance at the timer in the UI without

leaving the conversation or checking external tools

1. This would help with time tracking for billable work or just

personal productivity awareness

Additional Context

_No response_