Filter out reasoning items from previous turns (#5857)

Reduces request size and prevents 400 errors when switching between API
orgs.

Based on Responses API behavior described in
https://cookbook.openai.com/examples/responses_api/reasoning_items#caching

codex-rs/core/tests/common/responses.rs

@@ -68,6 +68,14 @@ impl ResponsesRequest {
             .clone()
     }
 
+    pub fn inputs_of_type(&self, ty: &str) -> Vec<Value> {
+        self.input()
+            .iter()
+            .filter(|item| item.get("type").and_then(Value::as_str) == Some(ty))
+            .cloned()
+            .collect()
+    }
+
     pub fn function_call_output(&self, call_id: &str) -> Value {
         self.call_output(call_id, "function_call_output")
     }