[FEATURE] Timestamp for claude code messages (also in VS Code extension)

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

While working with claude code I am frequently trying to understand:

• in which situation, claude code came to a certain finding (i.e. while debugging)
• where in the conversation I am reading (when scrolling back)
• what took claude code a lot of time and what less

Proposed Solution

For all these reasons it would be helpfull if claude code's messages in the conversation are time stamped. It makes it easier to reach conclusions on these questions.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

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Additional Context

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