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-protocol/src/jsonrpc_lite.rs

@@ -1,6 +1,7 @@
 //! We do not do true JSON-RPC 2.0, as we neither send nor expect the
 //! "jsonrpc": "2.0" field.
 
+use codex_protocol::protocol::W3cTraceContext;
 use schemars::JsonSchema;
 use serde::Deserialize;
 use serde::Serialize;
@@ -38,6 +39,10 @@ pub struct JSONRPCRequest {
     #[serde(default, skip_serializing_if = "Option::is_none")]
     #[ts(optional)]
     pub params: Option<serde_json::Value>,
+    /// Optional W3C Trace Context for distributed tracing.
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    #[ts(optional)]
+    pub trace: Option<W3cTraceContext>,
 }
 
 /// A notification which does not expect a response.