[Bug] Starting new session via /new reuses name of previously renamed session

Bug Description
I have noticed a bug with session name renaming, and have reproduced it a couple of times now.

What happened:
I renames a session for my use, for example, Bug Fix 1, and that session became huge in terms of context and size, so I had to start a new session, and so I used the new command to start a new conversion. But the new conversion took the same name I just provided to the earlier session.

So I had two sessions named Bug Fix 1

Example Image from my system

<img width="752" height="460" alt="Image" src="https://github.com/user-attachments/assets/5da2c8f7-043d-413f-b1f7-2585d7339ce2" />

Environment Info

• Platform: darwin
• Terminal: vscode
• Version: 2.1.299
• Feedback ID: 26babe0c-4386-4892-94fc-08c0b1ae2fd7