[tools] Add apply_patch tool (#2303)

## Summary
We've been seeing a number of issues and reports with our synthetic
`apply_patch` tool, e.g. #802. Let's make this a real tool - in my
anecdotal testing, it's critical for GPT-OSS models, but I'd like to
make it the standard across GPT-5 and codex models as well.

## Testing
- [x] Tested locally
- [x] Integration test

codex-rs/mcp-server/src/wire_format.rs

@@ -90,6 +90,10 @@ pub struct NewConversationParams {
     /// Whether to include the plan tool in the conversation.
     #[serde(skip_serializing_if = "Option::is_none")]
     pub include_plan_tool: Option<bool>,
+
+    /// Whether to include the apply patch tool in the conversation.
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub include_apply_patch_tool: Option<bool>,
 }
 
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq)]
@@ -241,6 +245,7 @@ mod tests {
                 config: None,
                 base_instructions: None,
                 include_plan_tool: None,
+                include_apply_patch_tool: None,
             },
         };
         assert_eq!(