[codex] Allow empty turn/start requests (#23409)

## Why

`turn/start` already accepts an input array on the wire, including an
empty array, but core treated empty input as a no-op before the turn
could reach the model. App-server clients need to be able to start a
real turn even when there is no new user message, for example to let the
model proceed from existing thread context.

## What changed

- Removed the `run_turn` early return that skipped empty-input turns
when there was no pending input.
- Kept empty active-turn steering rejected by moving the `steer_input`
empty-input check until after core has determined whether there is an
active regular turn.
- Empty regular turns now refresh `previous_turn_settings` like other
regular turns, so follow-up context injection state advances
consistently.
- Added an app-server v2 integration test proving `turn/start` with
`input: []` emits started/completed notifications, sends one Responses
request, and does not synthesize an empty user message.

## Validation

- `cargo test -p codex-app-server --test all
turn_start_with_empty_input_runs_model_request`

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

@@ -3143,10 +3143,6 @@ impl Session {
         expected_turn_id: Option<&str>,
         responsesapi_client_metadata: Option<HashMap<String, String>>,
     ) -> Result<String, SteerInputError> {
-        if input.is_empty() {
-            return Err(SteerInputError::EmptyInput);
-        }
-
         let mut active = self.active_turn.lock().await;
         let Some(active_turn) = active.as_mut() else {
             return Err(SteerInputError::NoActiveTurn(input));
@@ -3180,6 +3176,10 @@ impl Session {
             None => return Err(SteerInputError::NoActiveTurn(input)),
         }
 
+        if input.is_empty() {
+            return Err(SteerInputError::EmptyInput);
+        }
+
         if let Some(responsesapi_client_metadata) = responsesapi_client_metadata
             && let Some((_, active_task)) = active_turn.tasks.first()
         {