Browser permission: allow all sites for the current task only

No files, tests, or entry points are named. Start by locating the built-in browser's existing site-access permission flow and the task lifecycle it must follow. Done means the temporary option is shown, scoped to the browser instance and thread, revocable, absent from other tasks, expired after completion or cancellation, and does not change sensitive-action confirmations.

Feature request

Add a task-scoped browser permission option:

Allow all sites for this task

The permission should automatically expire when the current Work or Codex task finishes, is stopped, or is cancelled.

Current behavior

When the built-in browser reaches a new website, the user can:

• deny access;
• allow the website once; or
• allow access on all websites.

For tasks that legitimately need to move across several websites, Allow once can leave the task paused at an approval prompt while the user is away. Allow on all websites avoids those interruptions but grants a much broader and more persistent permission than the task requires.

Proposed behavior

Offer a middle option that:

1. allows the browser to visit new websites without repeated site-access prompts during the current task;
2. expires automatically at the end of that task;
3. remains scoped to the browser instance and thread that received the permission;
4. stays visible while active and can be revoked immediately by the user;
5. continues to require separate confirmation for sensitive actions such as signing in, submitting personal information, purchasing, changing permissions, or deleting data.

Why this helps

This would allow longer multi-site research, comparison, verification, and administrative workflows to continue unattended without requiring users to choose between repeated interruptions and a persistent global permission.

It would also make the permission model clearer:

• Allow once — one website access;
• Allow for this task — any necessary websites until this task ends;
• Always allow / allow on all websites — persistent broad access.

Suggested acceptance criteria

• The option appears alongside the existing site-access choices.
• The UI clearly shows that the permission is temporary and task-scoped.
• Starting another task does not inherit the permission.
• Resuming a completed or cancelled task requires fresh permission.
• Sensitive-action confirmations remain unchanged.