Forward client voice session IDs in realtime requests (#53784)

## What changed

Add optional `voiceSessionId` to realtime start parameters and forward it as the `voice-session-id` header for WebSocket, WebRTC, and existing-call transports. Keep this client-generated voice session identifier distinct from `realtimeSessionId`, which uses `x-session-id`.

## Testing

Extend serialization tests and add coverage for distinct session ID headers, WebRTC request forwarding, and existing-call handshake forwarding.

GitOrigin-RevId: cb558dbb9d438f2d34e281199a7e81fe5d33b879

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -4083,6 +4083,7 @@ mod tests {
                 realtime_end_instructions: Some("Resume normal text responses.".to_string()),
                 prompt: Some(Some("You are on a call".to_string())),
                 realtime_session_id: Some("sess_456".to_string()),
+                voice_session_id: Some("voice_789".to_string()),
                 transport: None,
                 version: Some(RealtimeConversationVersion::V3),
                 voice: Some(RealtimeVoice::Marin),
@@ -4122,6 +4123,7 @@ mod tests {
                     "realtimeEndInstructions": "Resume normal text responses.",
                     "prompt": "You are on a call",
                     "realtimeSessionId": "sess_456",
+                    "voiceSessionId": "voice_789",
                     "transport": null,
                     "version": "v3",
                     "voice": "marin"
@@ -4154,6 +4156,7 @@ mod tests {
                 realtime_end_instructions: None,
                 prompt: None,
                 realtime_session_id: None,
+                voice_session_id: None,
                 transport: None,
                 version: None,
                 voice: None,
@@ -4179,6 +4182,7 @@ mod tests {
                     "realtimeStartInstructions": null,
                     "realtimeEndInstructions": null,
                     "realtimeSessionId": null,
+                    "voiceSessionId": null,
                     "transport": null,
                     "version": null,
                     "voice": null
@@ -4207,6 +4211,7 @@ mod tests {
                 realtime_end_instructions: None,
                 prompt: Some(None),
                 realtime_session_id: None,
+                voice_session_id: None,
                 transport: None,
                 version: None,
                 voice: None,
@@ -4233,6 +4238,7 @@ mod tests {
                     "realtimeEndInstructions": null,
                     "prompt": null,
                     "realtimeSessionId": null,
+                    "voiceSessionId": null,
                     "transport": null,
                     "version": null,
                     "voice": null

codex-rs/app-server-protocol/src/protocol/v2/realtime.rs

@@ -257,6 +257,10 @@ pub struct ThreadRealtimeStartParams {
     pub prompt: Option<Option<String>>,
     #[ts(optional = nullable)]
     pub realtime_session_id: Option<String>,
+    /// Client-generated identifier for the product voice session. This is distinct from
+    /// `realtimeSessionId`.
+    #[ts(optional = nullable)]
+    pub voice_session_id: Option<String>,
     #[ts(optional = nullable)]
     pub transport: Option<ThreadRealtimeStartTransport>,
     /// Overrides the configured realtime protocol version for this session only.