[codex] Add response.processed websocket request (#21284)

## Summary

- Add a `response.processed` websocket request payload and sender for
Responses API websockets.
- Send `response.processed` from `try_run_sampling_request` after a
response completes, local turn processing succeeds, and the
session-owned feature flag is enabled.
- Add websocket coverage for both enabled and disabled feature-flag
behavior.

## Validation

- `just fmt`
- `cargo test -p codex-core response_processed`
- `cargo test -p codex-api responses_websocket`
- `cargo test -p codex-features
responses_websocket_response_processed_is_under_development`
- `git diff --check`
- `just fix -p codex-api -p codex-core -p codex-features`
- `git diff --check origin/main...HEAD`

codex-rs/codex-api/src/common.rs

@@ -239,6 +239,11 @@ 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>,
@@ -267,6 +272,8 @@ 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(