Feature request: Self-hosted Codex Desktop Web UI with LAN-only access and shared sessions

What variant of Codex are you using?

Desktop

What feature would you like to see?

I would like an official self-hosted web interface for Codex Desktop, accessible directly over a company LAN or VPN without an external relay.
My use case is running Codex Desktop on an always-on Mac mini and accessing it from my laptop. Company policy prohibits external remote-control relays, but permits internal network access.
Desired behavior:

• A browser UI close to the Codex Desktop experience.
• Shared conversations between the web UI and Desktop, including live progress, approvals, and follow-up messages.
• Tasks continue on the Mac mini when the browser disconnects or the laptop shuts down.
• Authentication and access control suitable for an internal deployment.
  The restriction concerns the remote-control transport, not company-approved model API access.
  VNC works, but a native web interface would provide a better workflow. A supported LAN-only mode for the existing remote-control feature would also address much of this need.

Additional information

No response

Start by surveying the existing Desktop remote-control feature and its session, approval, and authentication entry points; the issue names no files or tests. Define the LAN-only web UI scope, shared-session behavior, disconnect handling, and internal access controls before identifying implementation work and validation criteria.