[Bug] Fork command stores all forked conversation plans in single file

Bug Description
When I use the fork command, it stores all of the forked conversation's plans in the same file. I made a plan on 3 different forks and they all appended to the same plan file.

Environment Info

• Platform: darwin
• Terminal: iTerm.app
• Version: 2.1.34
• Feedback ID: d3d31c1b-22b1-4f9b-9bdb-d8c047f0010d

Errors

<img width="921" height="205" alt="Image" src="https://github.com/user-attachments/assets/fc0ffacb-6bdc-4247-ba31-aaceb1323aaa" />

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