feat(app-server): add tracing to all app-server APIs (#13285)

### Overview
This PR adds the first piece of tracing for app-server JSON-RPC
requests.

There are two main changes:
- JSON-RPC requests can now take an optional W3C trace context at the
top level via a `trace` field (`traceparent` / `tracestate`).
- app-server now creates a dedicated request span for every inbound
JSON-RPC request in `MessageProcessor`, and uses the request-level trace
context as the parent when present.

For compatibility with existing flows, app-server still falls back to
the TRACEPARENT env var when there is no request-level traceparent.

This PR is intentionally scoped to the app-server boundary. In a
followup, we'll actually propagate trace context through the async
handoff into core execution spans like run_turn, which will make
app-server traces much more useful.

### Spans
A few details on the app-server span shape:
- each inbound request gets its own server span
- span/resource names are based on the JSON-RPC method (`initialize`,
`thread/start`, `turn/start`, etc.)
- spans record transport (stdio vs websocket), request id, connection
id, and client name/version when available
- `initialize` stores client metadata in session state so later requests
on the same connection can reuse it

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

@@ -52,6 +52,7 @@ use tracing_subscriber::layer::SubscriberExt;
 use tracing_subscriber::registry::Registry;
 use tracing_subscriber::util::SubscriberInitExt;
 
+mod app_server_tracing;
 mod bespoke_event_handling;
 mod codex_message_processor;
 mod config_api;
@@ -447,7 +448,7 @@ pub async fn run_main_with_transport(
     let otel = codex_core::otel_init::build_provider(
         &config,
         env!("CARGO_PKG_VERSION"),
-        Some("codex_app_server"),
+        Some("codex-app-server"),
         default_analytics_enabled,
     )
     .map_err(|e| {
@@ -675,6 +676,7 @@ pub async fn run_main_with_transport(
                                             .process_request(
                                                 connection_id,
                                                 request,
+                                                transport,
                                                 &mut connection_state.session,
                                                 &connection_state.outbound_initialized,
                                             )