[codex] Use TurnInput for session task input (#24151)

## Why

The idea here is to erase the difference between initial and followup
inputs to a turn. Followup inputs are already represented as TurnInput.

Eventual goal is not to have explicit on task input at all and pull
everything from input Q.

## What Changed

- Changes `SessionTask::run` and the erased `AnySessionTask::run` path
to accept `Vec<TurnInput>`.
- Wraps user-submitted spawn input as `TurnInput::UserInput` at the
session task start boundary.
- Updates `run_turn` to record initial `TurnInput` using the same hook
and recording path used for pending input.
- Keeps review-specific conversion local to `ReviewTask`, where the
sub-Codex one-shot API still expects `Vec<UserInput>`.
- Moves the synthetic compact prompt into `CompactTask` and starts
compact tasks with empty task input.

## Validation

- `cargo check -p codex-core`
- `just test -p codex-core -E
'test(task_finish_emits_turn_item_lifecycle_for_leftover_pending_user_input)
| test(queued_response_items_for_next_turn_move_into_next_active_turn) |
test(steered_input_reopens_mailbox_delivery_for_current_turn)'`

codex-rs/core/src/session/handlers.rs

@@ -460,16 +460,8 @@ pub async fn reload_user_config(sess: &Arc<Session>) {
 pub async fn compact(sess: &Arc<Session>, sub_id: String) {
     let turn_context = sess.new_default_turn_with_sub_id(sub_id).await;
 
-    sess.spawn_task(
-        Arc::clone(&turn_context),
-        vec![UserInput::Text {
-            text: turn_context.compact_prompt().to_string(),
-            // Compaction prompt is synthesized; no UI element ranges to preserve.
-            text_elements: Vec::new(),
-        }],
-        CompactTask,
-    )
-    .await;
+    sess.spawn_task(Arc::clone(&turn_context), Vec::new(), CompactTask)
+        .await;
 }
 
 pub async fn thread_rollback(sess: &Arc<Session>, sub_id: String, num_turns: u32) {