[FEATURE] Cowork built-in browser: apply View → Zoom to the browser pane when it has focus (persisted, like Codex)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

This is about Cowork's built-in browser, the browser pane inside the Claude desktop app that Cowork uses for web tasks (Settings > Cowork > Preferred browser = "Built-in browser"; see https://support.claude.com/en/articles/16607400-use-the-built-in-browser-in-claude-cowork).

The desktop app's View → Zoom In / Zoom Out / Actual Size (Ctrl+= / Ctrl+- / Ctrl+0) scales the whole app. The built-in browser pane has no zoom of its own. The pane shares a narrow side panel, so most sites are cramped at 100%. The only fix today is to shrink the entire app, including the chat, which I don't want.

Proposed Solution

Extend the existing zoom commands rather than adding a new feature:

1. Focus-scoped routing. When the browser pane has focus, View → Zoom In/Out/Actual Size and their shortcuts change the pane's page zoom. Otherwise they change app zoom, as they do now.
2. Persistence. Remember the pane zoom level across pages, sessions and restarts, separately from app zoom. Set it to 80% once and it stays.
3. Visible state. Show a zoom badge (e.g. "80%") in the pane toolbar whenever it isn't 100%, and let a click reset it. Without this, it's unclear which surface a shortcut just changed.
4. Automation stays aligned. Claude's screenshot and click coordinates in the pane, and any annotate overlay, must account for the pane zoom factor.

Prior art: The Codex desktop app already routes its View-menu zoom commands to its embedded browser pane when the pane has focus (openai/codex#39713), and its built-in browser supports non-100% zoom (openai/codex#31454). The same issues show the pitfalls to avoid: routing that can't be seen (#39713) and overlay/click coordinates that drift at non-100% zoom (#31454). Points 3 and 4 above address those.

Alternative Solutions

• App-wide zoom scales the chat and everything else, not just the pane.
• Widening the pane changes the viewport, not the zoom.
• A separate zoom setting in the pane would be a second, parallel zoom system. Reusing View → Zoom keeps a single model.

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

Claude drives the browser pane for research and form work while I watch. At 80%, most sites fit the side panel. I want to press Ctrl+- twice with the pane focused, once, and have every later page and session open at 80%, while the chat stays at its own zoom.

Additional Context

• Surface: Cowork, built-in browser pane (Preferred browser = Built-in browser)
• Claude desktop app: 2.9939.2
• OS: Windows x64
• Codex prior art: https://github.com/openai/codex/issues/39713, https://github.com/openai/codex/issues/31454
• Related (closed/stale): #34998 (asked for pane zoom that resets each session, the opposite of this), #31964, #48157, #80507