[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/codex-api/src/endpoint/realtime_websocket/methods_common.rs

@@ -12,7 +12,6 @@ use crate::endpoint::realtime_websocket::protocol::RealtimeSessionMode;
 use crate::endpoint::realtime_websocket::protocol::SessionUpdateSession;
 
 pub(super) const REALTIME_AUDIO_SAMPLE_RATE: u32 = 24_000;
-pub(super) const REALTIME_AUDIO_FORMAT: &str = "audio/pcm";
 
 pub(super) fn normalized_session_mode(
     event_parser: RealtimeEventParser,