[stack 2/4] Align main realtime v2 wire and runtime flow (#14830)

## Stack Position
2/4. Built on top of #14828.

## Base
- #14828

## Unblocks
- #14829
- #14827

## Scope
- Port the realtime v2 wire parsing, session, app-server, and
conversation runtime behavior onto the split websocket-method base.
- Branch runtime behavior directly on the current realtime session kind
instead of parser-derived flow flags.
- Keep regression coverage in the existing e2e suites.

---------

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

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

@@ -39,6 +39,8 @@ pub(super) enum RealtimeOutboundMessage {
         handoff_id: String,
         output_text: String,
     },
+    #[serde(rename = "response.create")]
+    ResponseCreate,
     #[serde(rename = "session.update")]
     SessionUpdate { session: SessionUpdateSession },
     #[serde(rename = "conversation.item.create")]
@@ -48,12 +50,24 @@ pub(super) enum RealtimeOutboundMessage {
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct SessionUpdateSession {
     #[serde(rename = "type")]
-    pub(super) kind: String,
+    pub(super) r#type: SessionType,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub(super) instructions: Option<String>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub(super) output_modalities: Option<Vec<String>>,
     pub(super) audio: SessionAudio,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub(super) tools: Option<Vec<SessionFunctionTool>>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub(super) tool_choice: Option<String>,
+}
+
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum SessionType {
+    Quicksilver,
+    Realtime,
+    Transcription,
 }
 
 #[derive(Debug, Clone, Serialize)]
@@ -66,17 +80,29 @@ pub(super) struct SessionAudio {
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct SessionAudioInput {
     pub(super) format: SessionAudioFormat,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub(super) noise_reduction: Option<SessionNoiseReduction>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub(super) turn_detection: Option<SessionTurnDetection>,
 }
 
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct SessionAudioFormat {
     #[serde(rename = "type")]
-    pub(super) kind: String,
+    pub(super) r#type: AudioFormatType,
     pub(super) rate: u32,
 }
 
+#[derive(Debug, Clone, Copy, Serialize)]
+pub(super) enum AudioFormatType {
+    #[serde(rename = "audio/pcm")]
+    AudioPcm,
+}
+
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct SessionAudioOutput {
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub(super) format: Option<SessionAudioOutputFormat>,
     pub(super) voice: SessionAudioVoice,
 }
 
@@ -84,18 +110,64 @@ pub(super) struct SessionAudioOutput {
 pub(super) enum SessionAudioVoice {
     #[serde(rename = "fathom")]
     Fathom,
-    #[serde(rename = "alloy")]
-    Alloy,
+    #[serde(rename = "marin")]
+    Marin,
+}
+
+#[derive(Debug, Clone, Serialize)]
+pub(super) struct SessionNoiseReduction {
+    #[serde(rename = "type")]
+    pub(super) r#type: NoiseReductionType,
+}
+
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum NoiseReductionType {
+    NearField,
+}
+
+#[derive(Debug, Clone, Serialize)]
+pub(super) struct SessionTurnDetection {
+    #[serde(rename = "type")]
+    pub(super) r#type: TurnDetectionType,
+    pub(super) interrupt_response: bool,
+    pub(super) create_response: bool,
+}
+
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum TurnDetectionType {
+    ServerVad,
+}
+
+#[derive(Debug, Clone, Serialize)]
+pub(super) struct SessionAudioOutputFormat {
+    #[serde(rename = "type")]
+    pub(super) r#type: AudioFormatType,
+    pub(super) rate: u32,
 }
 
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct ConversationMessageItem {
     #[serde(rename = "type")]
-    pub(super) kind: String,
-    pub(super) role: String,
+    pub(super) r#type: ConversationItemType,
+    pub(super) role: ConversationRole,
     pub(super) content: Vec<ConversationItemContent>,
 }
 
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum ConversationItemType {
+    Message,
+    FunctionCallOutput,
+}
+
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum ConversationRole {
+    User,
+}
+
 #[derive(Debug, Clone, Serialize)]
 #[serde(untagged)]
 pub(super) enum ConversationItemPayload {
@@ -106,7 +178,7 @@ pub(super) enum ConversationItemPayload {
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct ConversationFunctionCallOutputItem {
     #[serde(rename = "type")]
-    pub(super) kind: String,
+    pub(super) r#type: ConversationItemType,
     pub(super) call_id: String,
     pub(super) output: String,
 }
@@ -114,19 +186,32 @@ pub(super) struct ConversationFunctionCallOutputItem {
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct ConversationItemContent {
     #[serde(rename = "type")]
-    pub(super) kind: String,
+    pub(super) r#type: ConversationContentType,
     pub(super) text: String,
 }
 
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum ConversationContentType {
+    Text,
+    InputText,
+}
+
 #[derive(Debug, Clone, Serialize)]
 pub(super) struct SessionFunctionTool {
     #[serde(rename = "type")]
-    pub(super) kind: String,
+    pub(super) r#type: SessionToolType,
     pub(super) name: String,
     pub(super) description: String,
     pub(super) parameters: Value,
 }
 
+#[derive(Debug, Clone, Copy, Serialize)]
+#[serde(rename_all = "snake_case")]
+pub(super) enum SessionToolType {
+    Function,
+}
+
 pub(super) fn parse_realtime_event(
     payload: &str,
     event_parser: RealtimeEventParser,