Remote Control: option to keep RC active without the status banner (VS Code)

Feature request

When Remote Control is active in the VS Code extension, a banner is pinned above the input box:

Remote Control is active · Continue here, on your phone, or at claude.ai/code

Clicking the × on the banner disconnects Remote Control entirely — there is no way to dismiss the banner while keeping RC active, and no setting in settings.json, /config, or an environment variable to suppress it.

Ask: an option to keep Remote Control active without the persistent banner — either a setting (e.g. remoteControl.hideBanner) or a dismiss behavior on × that hides the banner without disconnecting (with the state still visible somewhere less prominent, like the status bar).

Use case: Remote Control stays on all day as a background channel (steering long-running sessions from the phone while away), so the banner is permanent screen real estate above the prompt even when working locally.

Extension: Claude Code for VS Code, macOS (Darwin 25.5.0).