VS Code: moving chat from side panel to main window breaks modals and resets permissions

Description

When a Claude Code chat is moved from the VS Code side panel to the main editor window (via drag/detach), two things break:

1. Modals are destroyed mid-flow — any modal Claude is trying to display (e.g. permission prompts) never surfaces or is silently dropped. The operation Claude was attempting stalls or fails without feedback.

1. Permissions reset to system default — the active permission level reverts to the VS Code/system default ("ask before edits"), discarding the user's configured Claude Code default. This is a silent downgrade — nothing in the UI indicates the permission level changed.

Steps to reproduce

1. Start a Claude Code chat in the side panel with a non-default permission level configured (e.g. auto-approve edits).
2. Mid-session, drag/detach the chat panel into the main editor window.
3. Trigger an action that would show a modal (e.g. a file edit requiring approval).

Expected: Modal surfaces; permission level unchanged.
Actual: Modal never appears; permission level reverts to "ask before edits."

Notes

These two symptoms likely share a root cause — the panel detach probably tears down and re-creates the extension host context, losing both the modal lifecycle and the in-memory permission state. A single fix (preserving context across panel moves) would likely address both.

Environment

• Platform: macOS (Darwin 25.4.0)
• Editor: VS Code
• Extension: Claude Code VS Code extension