New conversations inherit renamed session title

Bug Description

After manually renaming a conversation to a custom title, all subsequently opened new conversations inherit that title instead of receiving their own auto-generated names.

Steps to Reproduce

1. Open Claude Code (VS Code extension or CLI)
2. Have an active conversation
3. Rename the conversation to a custom title (e.g., /rename fable-prompt or via UI rename)
4. Confirm rename succeeds
5. Open or create a new conversation
6. The new conversation displays with the old conversation's custom title instead of its own auto-generated title
7. All subsequent new conversations also inherit the same incorrect title

Expected Behavior

Each new conversation should receive its own unique auto-generated title based on its content/context. A manually-set title in one conversation should not propagate to new conversations.

Actual Behavior

New conversations display with the previously renamed conversation's title, leading to duplicate/confusing session names in the /resume list.

Environment

• Platform: VS Code extension (Windows 11)
• Claude Code version: Latest
• OS: Windows 11 Pro

Additional Context

This appears to be a conversation naming/state management issue where the renamed title is incorrectly applied as a default/template for new conversations instead of being scoped to a single session.

Related issues (different manifestations):

• #65010 — manual rename gets overwritten by auto-titling
• #31394 — /rename doesn't persist in /resume list
• #65361 — renamed session disappears from /resume