[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/core/tests/prompt_caching.rs

@@ -1,6 +1,9 @@
+#![allow(clippy::unwrap_used)]
+
 use codex_core::ConversationManager;
 use codex_core::ModelProviderInfo;
 use codex_core::built_in_model_providers;
+use codex_core::model_family::find_family_for_model;
 use codex_core::protocol::AskForApproval;
 use codex_core::protocol::EventMsg;
 use codex_core::protocol::InputItem;
@@ -25,8 +28,20 @@ fn sse_completed(id: &str) -> String {
     load_sse_fixture_with_id("tests/fixtures/completed_template.json", id)
 }
 
+fn assert_tool_names(body: &serde_json::Value, expected_names: &[&str]) {
+    assert_eq!(
+        body["tools"]
+            .as_array()
+            .unwrap()
+            .iter()
+            .map(|t| t["name"].as_str().unwrap().to_string())
+            .collect::<Vec<_>>(),
+        expected_names
+    );
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 4)]
-async fn default_system_instructions_contain_apply_patch() {
+async fn codex_mini_latest_tools() {
     use pretty_assertions::assert_eq;
 
     let server = MockServer::start().await;
@@ -58,6 +73,10 @@ async fn default_system_instructions_contain_apply_patch() {
 
     let conversation_manager =
         ConversationManager::with_auth(CodexAuth::from_api_key("Test API Key"));
+    config.include_apply_patch_tool = false;
+    config.model = "codex-mini-latest".to_string();
+    config.model_family = find_family_for_model("codex-mini-latest").unwrap();
+
     let codex = conversation_manager
         .new_conversation(config)
         .await
@@ -173,18 +192,6 @@ async fn prompt_tools_are_consistent_across_requests() {
     // our internal implementation is responsible for keeping tools in sync
     // with the OpenAI schema, so we just verify the tool presence here
     let expected_tools_names: &[&str] = &["shell", "update_plan", "apply_patch"];
-    fn assert_tool_names(body: &serde_json::Value, expected_names: &[&str]) {
-        assert_eq!(
-            body["tools"]
-                .as_array()
-                .unwrap()
-                .iter()
-                .map(|t| t["name"].as_str().unwrap().to_string())
-                .collect::<Vec<_>>(),
-            expected_names
-        );
-    }
-
     let body0 = requests[0].body_json::<serde_json::Value>().unwrap();
     assert_eq!(
         body0["instructions"],