[FEATURE] Auto create log file of claude cli session

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

For claude cli have ability to auto create a log file with timestamp in the file name.
I enjoy reviewing what was done during prior session.
When I ask for bash commands it would be nice to easily copy paste to my separate notes file.
Sometimes claude wipes out output. With a log file I hope that doesn't happen.
Interface: Hey Claude auto create a log file for each session.
What should be logged: Hopefully everything.
File name format: don't care much but this looks good: claude-YYYYMMDD-HHMMSS.log, hopefully in a subdirectory of current session named logs. Auto add to .gitignore

Proposed Solution

Is claude cli open source? If yes, maybe I can vibe code it.

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_