Plan upgrade breaks all open VS Code conversations

Description

Upgrading account plan while VS Code Claude Code extension conversations are open causes all existing conversations to become unresponsive (infinite spinner). This includes conversations that were idle and did not attempt to send any messages during the transition.

New conversations created after the upgrade work fine. CLI is unaffected.

Steps to Reproduce

1. Have multiple open Claude Code conversations in VS Code
2. Upgrade account plan (in this case, upgraded to Max plan)
3. All existing VS Code conversations become stuck/unresponsive
4. New conversations work normally

Expected Behavior

Existing idle conversations should remain functional after a plan change. At minimum, conversations that didn't attempt any API calls during the transition should not break.

Actual Behavior

All open conversations (including idle ones) become permanently stuck with an infinite spinner. They cannot be recovered, even after restarting VS Code.

Environment

• Claude Code version: 2.1.66 (both CLI and VS Code extension)
• OS: Windows 11 Pro
• VS Code: latest