Align main realtime v2 wire and runtime flow

Port the realtime v2 session, parser, app-server, and conversation runtime behavior onto the split websocket-method base without pulling in the startup-context or TUI playback slices.

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

codex-rs/app-server/tests/suite/v2/realtime_conversation.rs

@@ -135,6 +135,7 @@ async fn realtime_conversation_streams_v2_notifications() -> Result<()> {
                 sample_rate: 24_000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         })
         .await?;