[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/core/config.schema.json

@@ -523,6 +523,9 @@
             "request_rule": {
               "type": "boolean"
             },
+            "responses_websocket_response_processed": {
+              "type": "boolean"
+            },
             "responses_websockets": {
               "type": "boolean"
             },
@@ -4078,6 +4081,9 @@
         "request_rule": {
           "type": "boolean"
         },
+        "responses_websocket_response_processed": {
+          "type": "boolean"
+        },
         "responses_websockets": {
           "type": "boolean"
         },