Remove response.processed websocket request (#26447)

## Why

The Responses websocket client no longer needs to send a follow-up
`response.processed` request after a turn response has already been
recorded. Keeping that extra acknowledgement path adds feature-gated
control flow and a second websocket request shape that no longer carries
useful behavior.

## What Changed

- Removed the `response.processed` websocket request type and sender.
- Removed the `responses_websocket_response_processed` feature flag and
schema entry.
- Removed turn and remote-compaction plumbing that only tracked response
IDs to send the acknowledgement.
- Removed tests that existed solely to cover the deleted feature path.

## Validation

- `just fix -p codex-core -p codex-api -p codex-features`

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

@@ -1827,7 +1827,6 @@ async fn try_run_sampling_request(
         !sess.services.extensions.turn_item_contributors().is_empty();
     let mut active_item_is_streaming_to_client = false;
     let receiving_span = trace_span!("receiving_stream");
-    let mut completed_response_id: Option<String> = None;
     let outcome: CodexResult<SamplingRequestResult> = loop {
         let handle_responses = trace_span!(
             parent: &receiving_span,
@@ -2071,9 +2070,9 @@ async fn try_run_sampling_request(
                 sess.services.models_manager.refresh_if_new_etag(etag).await;
             }
             ResponseEvent::Completed {
-                response_id,
                 token_usage,
                 end_turn,
+                ..
             } => {
                 flush_assistant_text_segments_all(
                     &sess,
@@ -2089,7 +2088,6 @@ async fn try_run_sampling_request(
                 if let Some(false) = end_turn {
                     needs_follow_up = true;
                 }
-                completed_response_id = Some(response_id);
                 break Ok(SamplingRequestResult {
                     needs_follow_up,
                     last_agent_message,
@@ -2213,15 +2211,6 @@ async fn try_run_sampling_request(
     )
     .await;
 
-    if sess
-        .features
-        .enabled(Feature::ResponsesWebsocketResponseProcessed)
-        && outcome.is_ok()
-        && let Some(response_id) = completed_response_id.as_deref()
-    {
-        client_session.send_response_processed(response_id).await;
-    }
-
     drain_in_flight(&mut in_flight, sess.clone(), turn_context.clone()).await?;
 
     if should_emit_token_count {