[Feature Request] Toggle Claude Code session between terminal and native UI modes

Bug Description

Feature request: toggle an existing Claude Code session between terminal and native UI

The Claude Code: Use Terminal setting in the Cursor/VS Code extension controls which mode new sessions launch in, and toggling it
works fine for that. What's missing is the ability to move an existing, in-progress session between modes.

Each mode supports actions the other doesn't — for example:

• Pasting an image is supported in the native UI but not in the terminal.
• Exporting a transcript is supported in the terminal but not in the native UI.

Today, hitting one of these limitations mid-session means either losing the conversation context to start over in the other mode, or
doing without the action.

Requested: a command (palette entry / keybinding) like Claude Code: Move Session to Terminal and Claude Code: Move Session to Panel
that detaches the current session from its current surface and reattaches it to the other, preserving conversation history and
state.
Alternative: Support all commands in native UI

Environment: Cursor on macOS, SSH-connected to a Linux dev host.

Environment Info

• Platform: linux
• Terminal: cursor
• Version: 2.1.132
• Feedback ID: 48611c97-0232-4731-9f12-41f97cd34de3