Create independent TurnContexts (#5308)

The goal of this change:
1. Unify user input and user turn implementation.
2. Have a single place where turn/session setting overrides are applied.
3. Have a single place where turn context is created.
4. Create TurnContext only for actual turn and have a separate structure
for current session settings (reuse ConfigureSession)

codex-rs/core/tests/suite/prompt_caching.rs

@@ -507,7 +507,7 @@ async fn overrides_turn_context_but_keeps_cached_prefix_and_key_constant() {
     <root>{}</root>
   </writable_roots>
 </environment_context>"#,
-        writable.path().to_string_lossy()
+        writable.path().to_string_lossy(),
     );
     let expected_env_msg_2 = serde_json::json!({
         "type": "message",
@@ -866,15 +866,14 @@ async fn send_user_turn_with_changes_sends_environment_context() {
     ]);
     assert_eq!(body1["input"], expected_input_1);
 
-    let expected_env_msg_2 = text_user_input(format!(
+    let expected_env_msg_2 = text_user_input(
         r#"<environment_context>
-  <cwd>{}</cwd>
   <approval_policy>never</approval_policy>
   <sandbox_mode>danger-full-access</sandbox_mode>
   <network_access>enabled</network_access>
-</environment_context>"#,
-        default_cwd.to_string_lossy()
-    ));
+</environment_context>"#
+            .to_string(),
+    );
     let expected_user_message_2 = text_user_input("hello 2".to_string());
     let expected_input_2 = serde_json::Value::Array(vec![
         expected_ui_msg,