[FEATURE] VSCode Extension - Add support for /export command

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

I hope I can export a session with /export command on Claude Code VSCode just like Claude Code CLI easily

Proposed Solution

/export command in VSCode Extension
will output the session conversation that I can copy

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

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Additional Context

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