Add codex tool support for realtime v2 handoff (#14554)

- Advertise a `codex` function tool in realtime v2 session updates.
- Emit handoff replies as `function_call_output` items while keeping v1
behavior unchanged.
- Split realtime event parsing into explicit v1/v2 modules with shared
common helpers.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/codex-api/src/endpoint/realtime_websocket/protocol_common.rs

@@ -0,0 +1,71 @@
+use codex_protocol::protocol::RealtimeEvent;
+use codex_protocol::protocol::RealtimeTranscriptDelta;
+use serde_json::Value;
+use tracing::debug;
+
+pub(super) fn parse_realtime_payload(payload: &str, parser_name: &str) -> Option<(Value, String)> {
+    let parsed: Value = match serde_json::from_str(payload) {
+        Ok(message) => message,
+        Err(err) => {
+            debug!("failed to parse {parser_name} event: {err}, data: {payload}");
+            return None;
+        }
+    };
+
+    let message_type = match parsed.get("type").and_then(Value::as_str) {
+        Some(message_type) => message_type.to_string(),
+        None => {
+            debug!("received {parser_name} event without type field: {payload}");
+            return None;
+        }
+    };
+
+    Some((parsed, message_type))
+}
+
+pub(super) fn parse_session_updated_event(parsed: &Value) -> Option<RealtimeEvent> {
+    let session_id = parsed
+        .get("session")
+        .and_then(Value::as_object)
+        .and_then(|session| session.get("id"))
+        .and_then(Value::as_str)
+        .map(str::to_string)?;
+    let instructions = parsed
+        .get("session")
+        .and_then(Value::as_object)
+        .and_then(|session| session.get("instructions"))
+        .and_then(Value::as_str)
+        .map(str::to_string);
+    Some(RealtimeEvent::SessionUpdated {
+        session_id,
+        instructions,
+    })
+}
+
+pub(super) fn parse_transcript_delta_event(
+    parsed: &Value,
+    field: &str,
+) -> Option<RealtimeTranscriptDelta> {
+    parsed
+        .get(field)
+        .and_then(Value::as_str)
+        .map(str::to_string)
+        .map(|delta| RealtimeTranscriptDelta { delta })
+}
+
+pub(super) fn parse_error_event(parsed: &Value) -> Option<RealtimeEvent> {
+    parsed
+        .get("message")
+        .and_then(Value::as_str)
+        .map(str::to_string)
+        .or_else(|| {
+            parsed
+                .get("error")
+                .and_then(Value::as_object)
+                .and_then(|error| error.get("message"))
+                .and_then(Value::as_str)
+                .map(str::to_string)
+        })
+        .or_else(|| parsed.get("error").map(ToString::to_string))
+        .map(RealtimeEvent::Error)
+}