Feature request: Codex-style background computer control with concurrent window/session ownership

Problem

Claude's computer-control experience should match or exceed the current OpenAI Codex computer-use baseline.

The important capability is not just "Claude can click/type on my computer." It is that agent sessions can operate in the background while I continue working in the foreground, and that multiple sessions can safely control different windows at the same time.

Expected behavior

• A Claude Code / Claude Desktop agent session can control an assigned app/window in the background while the user continues using other apps normally.
• Multiple Claude sessions can run concurrently, each controlling a different target window/session without stealing focus from the others.
• The user can keep working in the foreground while background agent sessions continue making progress.
• Window/session ownership is explicit enough that one session does not unexpectedly interfere with another session or the user's active foreground work.
• The experience should be at least as seamless as OpenAI Codex's current computer-use behavior, because that is now the comparison point for users evaluating Claude Code.

Why this matters

This changes computer control from a novelty into a practical daily workflow. If each agent task monopolizes the user's screen/focus, the user cannot comfortably run several Claude Code sessions while continuing their own work. Codex has shown that background computer use and concurrent window control are achievable and useful. Claude Code should treat that as the baseline to match, then improve on it.

Use case

I want to start one Claude session that operates a browser or desktop app for a work task, start another session that controls a different app/window for a separate task, and still keep using my computer in the foreground. I should be able to inspect those sessions when needed, but they should not require me to stop using my machine while they work.