Move changing turn input functionalities to ConversationHistory (#5473)

We are doing some ad-hoc logic while dealing with conversation history.
Ideally, we shouldn't mutate `vec[responseitem]` manually at all and
should depend on `ConversationHistory` for those changes.

Those changes are:
- Adding input to the history
- Removing items from the history
- Correcting history

I am also adding some `error` logs for cases we shouldn't ideally face.
For example, we shouldn't be missing `toolcalls` or `outputs`. We
shouldn't hit `ContextWindowExceeded` while performing `compact`

This refactor will give us granular control over our context management.

codex-rs/core/src/codex/compact.rs

@@ -24,6 +24,7 @@ use codex_protocol::models::ResponseItem;
 use codex_protocol::protocol::RolloutItem;
 use codex_protocol::user_input::UserInput;
 use futures::prelude::*;
+use tracing::error;
 
 pub const SUMMARIZATION_PROMPT: &str = include_str!("../../templates/compact/prompt.md");
 const COMPACT_USER_MESSAGE_MAX_TOKENS: usize = 20_000;
@@ -64,9 +65,10 @@ async fn run_compact_task_inner(
     input: Vec<UserInput>,
 ) {
     let initial_input_for_turn: ResponseInputItem = ResponseInputItem::from(input);
-    let mut turn_input = sess
-        .turn_input_with_history(vec![initial_input_for_turn.clone().into()])
-        .await;
+
+    let mut history = sess.clone_history().await;
+    history.record_items(&[initial_input_for_turn.into()]);
+
     let mut truncated_count = 0usize;
 
     let max_retries = turn_context.client.get_provider().stream_max_retries();
@@ -83,6 +85,7 @@ async fn run_compact_task_inner(
     sess.persist_rollout_items(&[rollout_item]).await;
 
     loop {
+        let turn_input = history.get_history();
         let prompt = Prompt {
             input: turn_input.clone(),
             ..Default::default()
@@ -107,7 +110,11 @@ async fn run_compact_task_inner(
             }
             Err(e @ CodexErr::ContextWindowExceeded) => {
                 if turn_input.len() > 1 {
-                    turn_input.remove(0);
+                    // Trim from the beginning to preserve cache (prefix-based) and keep recent messages intact.
+                    error!(
+                        "Context window exceeded while compacting; removing oldest history item. Error: {e}"
+                    );
+                    history.remove_first_item();
                     truncated_count += 1;
                     retries = 0;
                     continue;