fix(app-server): emit turn/started only when turn actually starts (#13261)

This is a follow-up for https://github.com/openai/codex/pull/13047

## Why
We had a race where `turn/started` could be observed before the thread
had actually transitioned to `Active`. This was because we eagerly
emitted `turn/started` in the request handler for `turn/start` (and
`review/start`).

That was showing up as flaky `thread/resume` tests, but the real issue
was broader: a client could see `turn/started` and still get back an
idle thread immediately afterward.

The first idea was to eagerly call
`thread_watch_manager.note_turn_started(...)` from the `turn/start`
request path. That turns out to be unsafe, because
`submit(Op::UserInput)` only queues work. If a turn starts and completes
quickly, request-path bookkeeping can race with the real lifecycle
events and leave stale running state behind.

**The real fix** is to move `turn/started` to emit only after the turn
_actually_ starts, so we do that by waiting for the
`EventMsg::TurnStarted` notification emitted by codex core. We do this
for both `turn/start` and `review/start`.

I also verified this change is safe for our first-party codex apps -
they don't have any assumptions that `turn/started` is emitted before
the RPC response to `turn/start` (which is correct anyway).

I also removed `single_client_mode` since it isn't really necessary now.

## Testing
- `cargo test -p codex-app-server thread_resume -- --nocapture`
- `cargo test -p codex-app-server
'suite::v2::turn_start::turn_start_emits_notifications_and_accepts_model_override'
-- --exact --nocapture`
- `cargo test -p codex-app-server`

codex-rs/app-server/src/message_processor.rs

@@ -150,7 +150,6 @@ pub(crate) struct MessageProcessorArgs {
     pub(crate) outgoing: Arc<OutgoingMessageSender>,
     pub(crate) arg0_paths: Arg0DispatchPaths,
     pub(crate) config: Arc<Config>,
-    pub(crate) single_client_mode: bool,
     pub(crate) cli_overrides: Vec<(String, TomlValue)>,
     pub(crate) loader_overrides: LoaderOverrides,
     pub(crate) cloud_requirements: CloudRequirementsLoader,
@@ -166,7 +165,6 @@ impl MessageProcessor {
             outgoing,
             arg0_paths,
             config,
-            single_client_mode,
             cli_overrides,
             loader_overrides,
             cloud_requirements,
@@ -202,7 +200,6 @@ impl MessageProcessor {
             config: Arc::clone(&config),
             cli_overrides: cli_overrides.clone(),
             cloud_requirements: cloud_requirements.clone(),
-            single_client_mode,
             feedback,
         });
         let config_api = ConfigApi::new(