[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/common.rs

@@ -1577,6 +1577,7 @@ mod tests {
                     sample_rate: 24_000,
                     num_channels: 1,
                     samples_per_channel: Some(512),
+                    item_id: None,
                 },
             },
         );
@@ -1589,7 +1590,8 @@ mod tests {
                         "data": "AQID",
                         "sampleRate": 24000,
                         "numChannels": 1,
-                        "samplesPerChannel": 512
+                        "samplesPerChannel": 512,
+                        "itemId": null
                     }
                 }
             }),
@@ -1641,6 +1643,7 @@ mod tests {
                     sample_rate: 24_000,
                     num_channels: 1,
                     samples_per_channel: Some(512),
+                    item_id: None,
                 },
             },
         );