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/tests/suite/v2/analytics.rs

@@ -30,7 +30,7 @@ async fn app_server_default_analytics_disabled_without_flag() -> Result<()> {
     let provider = codex_core::otel_init::build_provider(
         &config,
         SERVICE_VERSION,
-        Some("codex_app_server"),
+        Some("codex-app-server"),
         false,
     )
     .map_err(|err| anyhow::anyhow!(err.to_string()))?;
@@ -55,7 +55,7 @@ async fn app_server_default_analytics_enabled_with_flag() -> Result<()> {
     let provider = codex_core::otel_init::build_provider(
         &config,
         SERVICE_VERSION,
-        Some("codex_app_server"),
+        Some("codex-app-server"),
         true,
     )
     .map_err(|err| anyhow::anyhow!(err.to_string()))?;

codex-rs/app-server/tests/suite/v2/connection_handling_websocket.rs

@@ -174,6 +174,7 @@ pub(super) async fn send_request(
         id: RequestId::Integer(id),
         method: method.to_string(),
         params,
+        trace: None,
     });
     send_jsonrpc(stream, message).await
 }