Preserve MCP trace context when tracing is disabled (#60506)

## Why

MCP requests need to retain inbound W3C trace context even when no OpenTelemetry tracing layer is installed.

## What changed

- Carry validated request trace context through app-server MCP tasks, connection startup, and resource listing tasks, while preferring active span context.
- Forward fallback `traceparent` and `tracestate` headers for MCP HTTP requests, including discovery and initialization.
- Use HTTP trace headers as a fallback for exec-server RPC calls when active span context is unavailable.

## Testing

Add an app-server integration test that disables trace exporting and verifies that `mcpServer/resource/read` forwards the inbound `traceparent` and `tracestate` to the MCP server.

GitOrigin-RevId: c886a55ce0a3992f1b2e04614efec80a20cb4b49

codex-rs/codex-mcp/src/connection_manager.rs

@@ -1097,7 +1097,8 @@ impl McpConnectionSet {
                 // Dormant servers must not hold the initial startup summary open.
                 deferred_workers.push(startup);
             } else {
-                eager_workers.push(startup.boxed());
+                let trace = codex_rmcp_client::McpRequestTrace::current();
+                eager_workers.push(trace.scope(startup).boxed());
             }
         }
         let manager = Self {

codex-rs/codex-mcp/src/connection_manager/resources.rs

@@ -12,6 +12,7 @@ use std::time::Duration;
 use anyhow::Context;
 use anyhow::Result;
 use anyhow::anyhow;
+use codex_rmcp_client::McpRequestTrace;
 use rmcp::model::ListResourceTemplatesResult;
 use rmcp::model::ListResourcesResult;
 use rmcp::model::PaginatedRequestParams;
@@ -57,7 +58,7 @@ impl McpConnectionSet {
                 continue;
             };
             let timeout = view.tool_timeout;
-            join_set.spawn(async move {
+            let task = async move {
                 let resources = collect_paginated("resources/list", timeout, |params| {
                     let client = client.clone();
                     async move {
@@ -67,7 +68,8 @@ impl McpConnectionSet {
                 })
                 .await;
                 (server_name, resources)
-            });
+            };
+            join_set.spawn(McpRequestTrace::current().scope(task));
         }
 
         let mut resources = HashMap::new();
@@ -101,7 +103,7 @@ impl McpConnectionSet {
                 continue;
             };
             let timeout = view.tool_timeout;
-            join_set.spawn(async move {
+            let task = async move {
                 let templates = collect_paginated("resources/templates/list", timeout, |params| {
                     let client = client.clone();
                     async move {
@@ -111,7 +113,8 @@ impl McpConnectionSet {
                 })
                 .await;
                 (server_name, templates)
-            });
+            };
+            join_set.spawn(McpRequestTrace::current().scope(task));
         }
 
         let mut templates = HashMap::new();

codex-rs/codex-mcp/src/rmcp_client.rs

@@ -103,7 +103,6 @@ use rmcp::model::Tool as RmcpTool;
 use tokio::sync::watch;
 use tokio::time::Instant as TokioInstant;
 use tokio_util::sync::CancellationToken;
-use tracing::Instrument;
 use tracing::instrument;
 use tracing::warn;
 
@@ -447,8 +446,7 @@ impl ManagedClientStartup {
             outcome
         };
         originator
-            .scope(Box::pin(startup))
-            .in_current_span()
+            .scope(codex_rmcp_client::McpRequestTrace::current().scope(Box::pin(startup)))
             .boxed()
             .shared()
     }