[Bug] Impeccable live starts with the Codex browser cursor visible

What happened?

When Impeccable live starts in Codex, the Codex browser cursor is visible on the page—the pointer with a blue glow shown in the screenshot. It draws attention away from the interface and is distracting during visual review.

Steps to reproduce

1. Start Impeccable live in Codex.
2. View the live page in the Codex browser.
3. Observe the glowing Codex browser cursor when the session starts.

Expected behavior

Live mode should start with the normal page cursor, without the Codex browser cursor overlay getting in the way of reviewing the interface.

Provider & environment

• Codex desktop app on macOS
• Impeccable live mode

Screenshot

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Issue prepared with AI assistance from the reporter's description and screenshot.