[Feature request][In-app Browser] Surface native webpage dialogs to agents

What variant of Codex are you using?

Codex app 26.818.61809 on macOS, using the in-app Browser control capability.

What feature would you like to see?

Surface native webpage alert, confirm, and prompt dialogs as structured in-app Browser state. The agent should receive the dialog type, message text, and origin, and should be able to accept or dismiss it. In-app Browser screenshots should also capture the visible dialog overlay.

If a dialog is blocking the page, Browser actions should report that condition instead of appearing to succeed or silently doing nothing.

Additional information

Minimal reproduction:

1. Open a webpage in the in-app Browser.
2. Submit an incomplete form that triggers a native JavaScript alert, or wait for a site-rendered session-extension modal.
3. The human can see the dialog and its message.
4. Structured Browser control can report no active dialog, expose only the underlying DOM, or time out when clicking the visible button.
5. The agent cannot reliably read or dismiss the dialog and may incorrectly infer that the previous action had no effect.

Expected behavior:

• Emit a dialog-open event containing type, message, and origin for native dialogs.
• Make native dialogs available through the structured dialog API until accepted or dismissed.
• Capture visible native and site-rendered modal overlays in in-app Browser screenshots.
• Report an explicit blocking-dialog condition when underlying-page actions cannot proceed.
• Preserve this behavior for unattended workflows where the user is away from the computer.

Important scope distinction: screen-level Computer Use can see these rendered dialogs. The gap is specifically in the in-app Browser structured state and interaction layer. This is also distinct from #37855, which concerns clicking a button in a separate Chrome popup window.

Start by tracing the in-app Browser structured state and interaction layer described in the issue, keeping it separate from screen-level Computer Use and the Chrome popup work in #37855. Define completion against the listed expected behavior: dialog events and controls, screenshot overlays, and an explicit blocking-dialog condition for unattended workflows.