Codex App: allow the browser panel to be docked on the left (← → side toggle, persisted per workspace)

What variant of Codex are you using?

Codex App (Desktop), current release.

What feature would you like to see?

Please allow the browser panel (side panel) to be docked on either side of the conversation, with a quick way to swap.

This is a narrow, shippable subset of #32444 (configurable workspace layouts); it also touches #37429 (persist layout) and #20236 (browser panel width per workspace).

Ideally:

• A visible ← → toggle in the browser panel header to swap sides instantly
• View → Browser panel position → Left / Right
• Remember the choice globally or per workspace
• Preserve the panel width when switching sides
• Expose the action in the command palette

Why

I'm doing a lot of work with WebMCP and preparing an entry for the OpenAI WebMCP Hackathon. For this workflow I strongly prefer the browser panel on the left and the conversation on the right: it makes the website the primary working surface, with ChatGPT/Codex acting as the agent sidebar — the interaction model people already understand from browser extensions.

The current chat-left/browser-right arrangement makes the browser feel like supporting material. During WebMCP use, however, the browser is the object being operated on: users need to watch page state, Site Tool activity, changes and confirmations while continuing the conversation alongside it.

I think this would materially improve the human–agent experience for WebMCP, rather than being merely cosmetic customization.

Start at the Codex App browser panel header and the existing workspace-layout and command-palette entry points; the issue names no files or tests. Done means the panel can switch between left and right, the position can be selected from View and the command palette, the choice is persisted, and the width is preserved when moving it.