[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/app-server-protocol/src/protocol/v2.rs

@@ -3659,6 +3659,7 @@ pub struct ThreadRealtimeAudioChunk {
     pub sample_rate: u32,
     pub num_channels: u16,
     pub samples_per_channel: Option<u32>,
+    pub item_id: Option<String>,
 }
 
 impl From<CoreRealtimeAudioFrame> for ThreadRealtimeAudioChunk {
@@ -3668,12 +3669,14 @@ impl From<CoreRealtimeAudioFrame> for ThreadRealtimeAudioChunk {
             sample_rate,
             num_channels,
             samples_per_channel,
+            item_id,
         } = value;
         Self {
             data,
             sample_rate,
             num_channels,
             samples_per_channel,
+            item_id,
         }
     }
 }
@@ -3685,12 +3688,14 @@ impl From<ThreadRealtimeAudioChunk> for CoreRealtimeAudioFrame {
             sample_rate,
             num_channels,
             samples_per_channel,
+            item_id,
         } = value;
         Self {
             data,
             sample_rate,
             num_channels,
             samples_per_channel,
+            item_id,
         }
     }
 }