[apply_patch] freeform apply_patch tool (#2576)

## Summary
GPT-5 introduced the concept of [custom
tools](https://platform.openai.com/docs/guides/function-calling#custom-tools),
which allow the model to send a raw string result back, simplifying
json-escape issues. We are migrating gpt-5 to use this by default.

However, gpt-oss models do not support custom tools, only normal
functions. So we keep both tool definitions, and provide whichever one
the model family supports.

## Testing
- [x] Tested locally with various models
- [x] Unit tests pass

codex-rs/exec/tests/apply_patch.rs

@@ -123,6 +123,155 @@ async fn test_apply_patch_tool() -> anyhow::Result<()> {
     // Start a mock model server
     let server = MockServer::start().await;
 
+    // First response: model calls apply_patch to create test.md
+    let first = ResponseTemplate::new(200)
+        .insert_header("content-type", "text/event-stream")
+        .set_body_raw(
+            load_sse_fixture_with_id_from_str(SSE_TOOL_CALL_ADD, "call1"),
+            "text/event-stream",
+        );
+
+    Mock::given(method("POST"))
+        // .and(path("/v1/responses"))
+        .respond_with(first)
+        .up_to_n_times(1)
+        .mount(&server)
+        .await;
+
+    // Second response: model calls apply_patch to update test.md
+    let second = ResponseTemplate::new(200)
+        .insert_header("content-type", "text/event-stream")
+        .set_body_raw(
+            load_sse_fixture_with_id_from_str(SSE_TOOL_CALL_UPDATE, "call2"),
+            "text/event-stream",
+        );
+
+    Mock::given(method("POST"))
+        .and(path("/v1/responses"))
+        .respond_with(second)
+        .up_to_n_times(1)
+        .mount(&server)
+        .await;
+
+    let final_completed = ResponseTemplate::new(200)
+        .insert_header("content-type", "text/event-stream")
+        .set_body_raw(
+            load_sse_fixture_with_id_from_str(SSE_TOOL_CALL_COMPLETED, "resp3"),
+            "text/event-stream",
+        );
+
+    Mock::given(method("POST"))
+        .and(path("/v1/responses"))
+        .respond_with(final_completed)
+        .expect(1)
+        .mount(&server)
+        .await;
+
+    let tmp_cwd = TempDir::new().unwrap();
+    Command::cargo_bin("codex-exec")
+        .context("should find binary for codex-exec")?
+        .current_dir(tmp_cwd.path())
+        .env("CODEX_HOME", tmp_cwd.path())
+        .env("OPENAI_API_KEY", "dummy")
+        .env("OPENAI_BASE_URL", format!("{}/v1", server.uri()))
+        .arg("--skip-git-repo-check")
+        .arg("-s")
+        .arg("workspace-write")
+        .arg("foo")
+        .assert()
+        .success();
+
+    // Verify final file contents
+    let final_path = tmp_cwd.path().join("test.md");
+    let contents = std::fs::read_to_string(&final_path)
+        .unwrap_or_else(|e| panic!("failed reading {}: {e}", final_path.display()));
+    assert_eq!(contents, "Final text\n");
+    Ok(())
+}
+
+#[cfg(not(target_os = "windows"))]
+#[tokio::test]
+async fn test_apply_patch_freeform_tool() -> anyhow::Result<()> {
+    use core_test_support::load_sse_fixture_with_id_from_str;
+    use tempfile::TempDir;
+    use wiremock::Mock;
+    use wiremock::MockServer;
+    use wiremock::ResponseTemplate;
+    use wiremock::matchers::method;
+    use wiremock::matchers::path;
+
+    const SSE_TOOL_CALL_ADD: &str = r#"[
+  {
+    "type": "response.output_item.done",
+    "item": {
+      "type": "custom_tool_call",
+      "name": "apply_patch",
+      "input": "*** Begin Patch\n*** Add File: test.md\n+Hello world\n*** End Patch",
+      "call_id": "__ID__"
+    }
+  },
+  {
+    "type": "response.completed",
+    "response": {
+      "id": "__ID__",
+      "usage": {
+        "input_tokens": 0,
+        "input_tokens_details": null,
+        "output_tokens": 0,
+        "output_tokens_details": null,
+        "total_tokens": 0
+      },
+      "output": []
+    }
+  }
+]"#;
+
+    const SSE_TOOL_CALL_UPDATE: &str = r#"[
+  {
+    "type": "response.output_item.done",
+    "item": {
+      "type": "custom_tool_call",
+      "name": "apply_patch",
+      "input": "*** Begin Patch\n*** Update File: test.md\n@@\n-Hello world\n+Final text\n*** End Patch",
+      "call_id": "__ID__"
+    }
+  },
+  {
+    "type": "response.completed",
+    "response": {
+      "id": "__ID__",
+      "usage": {
+        "input_tokens": 0,
+        "input_tokens_details": null,
+        "output_tokens": 0,
+        "output_tokens_details": null,
+        "total_tokens": 0
+      },
+      "output": []
+    }
+  }
+]"#;
+
+    const SSE_TOOL_CALL_COMPLETED: &str = r#"[
+  {
+    "type": "response.completed",
+    "response": {
+      "id": "__ID__",
+      "usage": {
+        "input_tokens": 0,
+        "input_tokens_details": null,
+        "output_tokens": 0,
+        "output_tokens_details": null,
+        "total_tokens": 0
+      },
+      "output": []
+    }
+  }
+]"#;
+
+    // Start a mock model server
+    let server = MockServer::start().await;
+
     // First response: model calls apply_patch to create test.md
     let first = ResponseTemplate::new(200)
         .insert_header("content-type", "text/event-stream")