feat(core) Introduce Feature::RequestPermissions (#11871)

## Summary
Introduces the initial implementation of Feature::RequestPermissions.
RequestPermissions allows the model to request that a command be run
inside the sandbox, with additional permissions, like writing to a
specific folder. Eventually this will include other rules as well, and
the ability to persist these permissions, but this PR is already quite
large - let's get the core flow working and go from there!

<img width="1279" height="541" alt="Screenshot 2026-02-15 at 2 26 22 PM"
src="https://github.com/user-attachments/assets/0ee3ec0f-02ec-4509-91a2-809ac80be368"
/>

## Testing
- [x] Added tests
- [x] Tested locally
- [x] Feature

codex-rs/protocol/src/prompts/permissions/approval_policy/on_request_rule_request_permission.md

@@ -0,0 +1,30 @@
+# Permission Requests
+
+Commands may require user approval before execution. Prefer requesting sandboxed additional permissions instead of asking to run fully outside the sandbox.
+
+## Preferred request mode
+
+When you need extra filesystem access for one command, use:
+
+- `sandbox_permissions: "with_additional_permissions"`
+- `additional_permissions` with one or both fields:
+  - `fs_read`: list of paths that need read access
+  - `fs_write`: list of paths that need write access
+
+This keeps execution inside the current sandbox policy, while adding only the requested permissions for that command, unless an exec-policy allow rule applies and authorizes running the command outside the sandbox.
+
+If the command already matches an exec-policy allow rule, the command can be auto-approved without an extra prompt. In that case, exec-policy allow behavior (including any sandbox bypass) takes precedence.
+
+## Escalation Requests
+
+Use full escalation only when sandboxed additional permissions cannot satisfy the task.
+
+- `sandbox_permissions: "require_escalated"`
+- Include `justification` as a short question asking for approval.
+- Optionally include `prefix_rule` to suggest a reusable allow rule.
+
+## Command segmentation reminder
+
+The command string is split into independent command segments at shell control operators, including pipes (`|`), logical operators (`&&`, `||`), command separators (`;`), and subshell boundaries (`(...)`, `$()`).
+
+Each segment is evaluated independently for sandbox restrictions and approval requirements.