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/codex-api/src/common.rs

@@ -239,11 +239,6 @@ pub struct ResponseCreateWsRequest {
     pub client_metadata: Option<HashMap<String, String>>,
 }
 
-#[derive(Debug, Serialize)]
-pub struct ResponseProcessedWsRequest {
-    pub response_id: String,
-}
-
 pub fn response_create_client_metadata(
     client_metadata: Option<HashMap<String, String>>,
     trace: Option<&W3cTraceContext>,
@@ -272,8 +267,6 @@ pub fn response_create_client_metadata(
 pub enum ResponsesWsRequest {
     #[serde(rename = "response.create")]
     ResponseCreate(ResponseCreateWsRequest),
-    #[serde(rename = "response.processed")]
-    ResponseProcessed(ResponseProcessedWsRequest),
 }
 
 pub fn create_text_param_for_request(