Route MCP auth discovery through runtime HTTP clients (#35239)

## Why

MCP authentication checks need to use the same HTTP routing as the MCP
transport so servers reached through configured proxies can be discovered
reliably.

## What changed

- Resolve OAuth discovery and authentication status through each server's
  runtime HTTP client for both local and managed environments.
- Keep local discovery capped at five seconds while allowing explicit login
  requests to retain their requested timeout.
- Resolve refreshed MCP configuration and its runtime context from the same
  snapshot.

## Testing

- Cover OAuth discovery through an environment proxy and macOS system proxy
  resolution.
- Cover proxied MCP startup and runtime refresh with updated authorization
  headers.
- Verify capped and preserved OAuth discovery timeout policies.

GitOrigin-RevId: 461fb1d4786e547df8b1e6b2215a8ac40438a3aa

codex-rs/app-server/src/request_processors/mcp_processor.rs

@@ -172,8 +172,12 @@ impl McpRequestProcessor {
             })?;
 
         let discovered_scopes = if scopes.is_none() && server.scopes.is_none() {
-            discover_supported_scopes_with_http_client(&server.transport, Arc::clone(&http_client))
-                .await
+            discover_supported_scopes_with_http_client(
+                &server.transport,
+                Arc::clone(&http_client),
+                codex_rmcp_client::OAuthDiscoveryTimeout::Requested,
+            )
+            .await
         } else {
             None
         };
@@ -250,11 +254,7 @@ impl McpRequestProcessor {
         let mcp_manager = self.thread_manager.mcp_manager();
         let auth = self.auth_manager.auth().await;
         let (mcp_config, runtime_context) = match thread {
-            Some(thread) => {
-                let mcp_config = thread.runtime_mcp_config(&config).await;
-                let (_, runtime_context) = thread.current_mcp_config_and_runtime_context().await;
-                (mcp_config, runtime_context)
-            }
+            Some(thread) => thread.runtime_mcp_config_and_context(&config).await,
             None => {
                 let mcp_config = mcp_manager.runtime_config(&config).await;
                 let runtime_context = McpRuntimeContext::new(