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/core/config.schema.json

@@ -370,6 +370,9 @@
             "remote_models": {
               "type": "boolean"
             },
+            "request_permissions": {
+              "type": "boolean"
+            },
             "request_rule": {
               "type": "boolean"
             },
@@ -1657,6 +1660,9 @@
         "remote_models": {
           "type": "boolean"
         },
+        "request_permissions": {
+          "type": "boolean"
+        },
         "request_rule": {
           "type": "boolean"
         },