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/features/src/lib.rs

@@ -207,8 +207,6 @@ pub enum Feature {
     RealtimeConversation,
     /// Prevent idle system sleep while a turn is actively running.
     PreventIdleSleep,
-    /// Send `response.processed` over Responses API websockets after a turn response is recorded.
-    ResponsesWebsocketResponseProcessed,
     /// Enable remote compaction v2 over the normal Responses API.
     RemoteCompactionV2,
     /// Enable workspace dependency support.
@@ -1228,12 +1226,6 @@ pub const FEATURES: &[FeatureSpec] = &[
         stage: Stage::Removed,
         default_enabled: false,
     },
-    FeatureSpec {
-        id: Feature::ResponsesWebsocketResponseProcessed,
-        key: "responses_websocket_response_processed",
-        stage: Stage::UnderDevelopment,
-        default_enabled: false,
-    },
     FeatureSpec {
         id: Feature::RemoteCompactionV2,
         key: "remote_compaction_v2",

codex-rs/features/src/tests.rs

@@ -146,22 +146,6 @@ fn remote_compaction_v2_is_under_development() {
     );
 }
 
-#[test]
-fn responses_websocket_response_processed_is_under_development() {
-    assert_eq!(
-        Feature::ResponsesWebsocketResponseProcessed.stage(),
-        Stage::UnderDevelopment
-    );
-    assert_eq!(
-        Feature::ResponsesWebsocketResponseProcessed.default_enabled(),
-        false
-    );
-    assert_eq!(
-        feature_for_key("responses_websocket_response_processed"),
-        Some(Feature::ResponsesWebsocketResponseProcessed)
-    );
-}
-
 #[test]
 fn terminal_resize_reflow_is_experimental_and_enabled_by_default() {
     assert_eq!(