[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/core/tests/suite/realtime_conversation.rs

@@ -176,6 +176,7 @@ async fn conversation_start_audio_text_close_round_trip() -> Result<()> {
                 sample_rate: 24000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         }))
         .await?;
@@ -409,6 +410,7 @@ async fn conversation_audio_before_start_emits_error() -> Result<()> {
                 sample_rate: 24000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         }))
         .await?;
@@ -518,6 +520,7 @@ async fn conversation_second_start_replaces_runtime() -> Result<()> {
                 sample_rate: 24000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         }))
         .await?;
@@ -1469,6 +1472,7 @@ async fn inbound_handoff_request_clears_active_transcript_after_each_handoff() -
                 sample_rate: 24000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         }))
         .await?;
@@ -1954,6 +1958,7 @@ async fn inbound_handoff_request_steers_active_turn() -> Result<()> {
                 sample_rate: 24000,
                 num_channels: 1,
                 samples_per_channel: Some(480),
+                item_id: None,
             },
         }))
         .await?;