Add experimental turn additional context (#24154)

## Summary

Adds experimental `additionalContext` support to `turn/start` and
`turn/steer` so clients can provide ephemeral external context, such as
browser or automation state, without turning that plumbing into a
visible user prompt or triggering user-prompt lifecycle behavior.

## API Shape

The parameter shape is:

```ts
additionalContext?: Record<string, {
  value: string
  kind: "untrusted" | "application"
}> | null
```

Example:

```json
{
  "additionalContext": {
    "browser_info": {
      "value": "Active tab is CI failures.",
      "kind": "untrusted"
    },
    "automation_info": {
      "value": "CI rerun is in progress.",
      "kind": "application"
    }
  }
}
```

The keys are opaque and caller-defined.

## Context Injection

When provided, accepted entries are inserted into model context as
hidden contextual message items, not as visible thread user-message
items.

`kind: "untrusted"` entries are inserted with role `user`:

```text
<external_${key}>${value}</external_${key}>
```

`kind: "application"` entries are inserted with role `developer`:

```text
<${key}>${value}</${key}>
```

Values are not escaped. Each value is truncated to 1k approximate tokens
before wrapping.

For `turn/start`, accepted additional context is inserted before normal
user input. For `turn/steer`, additional context is merged only when the
steer includes non-empty user input; context-only steers still reject as
empty input.

## Dedupe Strategy

`AdditionalContextStore` lives on session state and stores the latest
complete additional-context map.

Each `turn/start` or non-empty `turn/steer` treats its
`additionalContext` as the current complete set of values. Entries are
injected only when the key is new or the exact entry for that key
changed, including `value` or `kind`. After merging, the store is
replaced with the provided map, so omitted keys are removed from the
retained set and can be injected again later if reintroduced.

Omitting `additionalContext`, passing `null`, or passing an empty object
resets the store to empty and injects nothing.

## What Changed

- Threads experimental v2 `additionalContext` through app-server into
core turn start and steer handling.
- Adds separate contextual fragment types for untrusted user-role
context and application developer-role context.
- Uses pending response input items so additional context can be
combined with normal user input without treating it as prompt text.
- Adds integration coverage for start/steer flow, role routing,
dedupe/reset behavior, deletion/re-add behavior, hook-blocked input
behavior, empty context-only steer rejection, external-fragment marker
matching, and truncation.

codex-rs/app-server-protocol/schema/json/ClientRequest.json

@@ -12,6 +12,28 @@
       ],
       "type": "string"
     },
+    "AdditionalContextEntry": {
+      "properties": {
+        "kind": {
+          "$ref": "#/definitions/AdditionalContextKind"
+        },
+        "value": {
+          "type": "string"
+        }
+      },
+      "required": [
+        "kind",
+        "value"
+      ],
+      "type": "object"
+    },
+    "AdditionalContextKind": {
+      "enum": [
+        "untrusted",
+        "application"
+      ],
+      "type": "string"
+    },
     "ApprovalsReviewer": {
       "description": "Configures who approval requests are routed to for review. Examples include sandbox escapes, blocked network access, MCP approval prompts, and ARC escalations. Defaults to `user`. `auto_review` uses a carefully prompted subagent to gather relevant context and apply a risk-based decision framework before approving or denying the request. The legacy value `guardian_subagent` is accepted for compatibility.",
       "enum": [