fix(codex): support exec optimizer backend

docs/guideline.html

@@ -394,7 +394,7 @@ python scripts/train.py --config configs/searchqa/default.yaml</code></pre>
           <tr><td><code>claude_chat</code></td><td>Yes</td><td>Yes</td><td>Runs an installed, authenticated Claude Code CLI via <code>claude -p</code>; not a direct Anthropic API client.</td></tr>
           <tr><td><code>qwen_chat</code></td><td>Yes</td><td>Yes</td><td>Local or hosted Qwen-compatible server.</td></tr>
           <tr><td><code>minimax_chat</code></td><td>Yes</td><td>Yes</td><td>MiniMax chat endpoint.</td></tr>
-          <tr><td><code>codex_exec</code></td><td>No</td><td>Supported adapters only</td><td>Executes Codex as a target agent.</td></tr>
+          <tr><td><code>codex_exec</code></td><td>Yes</td><td>Supported adapters only</td><td>Executes Codex for optimizer calls and as a target agent where supported.</td></tr>
           <tr><td><code>claude_code_exec</code></td><td>No</td><td>Supported adapters only</td><td>Executes Claude Code as a target agent.</td></tr>
         </tbody>
       </table>

docs/reference/api.md

@@ -190,7 +190,7 @@ not via a base class subclass. Supported values (as of this writing):
 | `qwen_chat` | ✓ | ✓ |
 | `minimax_chat` | ✓ | ✓ |
 | `openai_compatible` | ✓ | ✓ |
-| `codex_exec` | — | ✓ |
+| `codex_exec` | ✓ | ✓ |
 | `claude_code_exec` | — | ✓ |
 
 See `skillopt/model/backend_config.py` for the live whitelist and

docs/reference/config.md

@@ -16,7 +16,7 @@ selecting the generic OpenAI-compatible backend.
 | `claude_chat` | ✓ | ✓ |
 | `qwen_chat` | ✓ | ✓ |
 | `minimax_chat` | ✓ | ✓ |
-| `codex_exec` | — | ✓ |
+| `codex_exec` | ✓ | ✓ |
 | `claude_code_exec` | — | ✓ |
 
 MiniMax currently has one shared deployment. `model.minimax_model` is applied
@@ -28,7 +28,7 @@ MiniMax optimizer model and a different target model.
 | `model.backend` | str | `azure_openai` | Backward-compatible high-level run label |
 | `model.optimizer` | str | `gpt-5.5` | Optimizer deployment/model |
 | `model.target` | str | `gpt-5.5` | Target deployment/model |
-| `model.optimizer_backend` | str | `openai_chat` | Optimizer client path; chat backends only |
+| `model.optimizer_backend` | str | `openai_chat` | Optimizer client path; chat backends plus `codex_exec` |
 | `model.target_backend` | str | `openai_chat` | Target client path; chat or exec backend |
 | `model.reasoning_effort` | str | `medium` | Shared reasoning effort |
 | `model.rewrite_reasoning_effort` | str | empty | Optional full-rewrite effort override |