[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/tests.rs

@@ -5738,7 +5738,7 @@ async fn spawn_task_turn_span_inherits_dispatch_trace_context() {
             self: Arc<Self>,
             _session: Arc<SessionTaskContext>,
             _ctx: Arc<TurnContext>,
-            _input: Vec<UserInput>,
+            _input: Vec<TurnInput>,
             _cancellation_token: CancellationToken,
         ) -> Option<String> {
             let mut trace = self
@@ -7814,7 +7814,7 @@ impl SessionTask for NeverEndingTask {
         self: Arc<Self>,
         _session: Arc<SessionTaskContext>,
         _ctx: Arc<TurnContext>,
-        _input: Vec<UserInput>,
+        _input: Vec<TurnInput>,
         cancellation_token: CancellationToken,
     ) -> Option<String> {
         if self.listen_to_cancellation_token {
@@ -7843,7 +7843,7 @@ impl SessionTask for GuardianDeniedApprovalTask {
         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();