[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/tui/src/voice.rs

@@ -428,6 +428,7 @@ fn send_realtime_audio_chunk(
                 sample_rate: MODEL_AUDIO_SAMPLE_RATE,
                 num_channels: MODEL_AUDIO_CHANNELS,
                 samples_per_channel: Some(samples_per_channel),
+                item_id: None,
             },
         },
     )));