[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/tasks/compact.rs

@@ -2,6 +2,7 @@ use std::sync::Arc;
 
 use super::SessionTask;
 use super::SessionTaskContext;
+use crate::session::TurnInput;
 use crate::session::turn_context::TurnContext;
 use crate::state::TaskKind;
 use codex_protocol::user_input::UserInput;
@@ -23,7 +24,7 @@ impl SessionTask for CompactTask {
         self: Arc<Self>,
         session: Arc<SessionTaskContext>,
         ctx: Arc<TurnContext>,
-        input: Vec<UserInput>,
+        _input: Vec<TurnInput>,
         _cancellation_token: CancellationToken,
     ) -> Option<String> {
         let session = session.clone_session();
@@ -47,6 +48,11 @@ impl SessionTask for CompactTask {
                 /*inc*/ 1,
                 &[("type", "local")],
             );
+            let input = vec![UserInput::Text {
+                text: ctx.compact_prompt().to_string(),
+                // Compaction prompt is synthesized; no UI element ranges to preserve.
+                text_elements: Vec::new(),
+            }];
             crate::compact::run_compact_task(session.clone(), ctx, input).await
         };
         None