Forward session and turn headers to MCP HTTP requests (#15011)

## Summary
- forward request-scoped task headers through MCP tool metadata lookups
and tool calls
- apply those headers to streamable HTTP initialize, tools/list, and
tools/call requests
- update affected rmcp/core tests for the new request_headers plumbing

## Testing
- cargo test -p codex-rmcp-client
- cargo test -p codex-core (fails on pre-existing unrelated error in
core/src/auth_env_telemetry.rs: missing websocket_connect_timeout_ms in
ModelProviderInfo initializer)
- just fix -p codex-rmcp-client
- just fix -p codex-core (hits the same unrelated auth_env_telemetry.rs
error)
- just fmt

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/src/tasks/mod.rs

@@ -153,6 +153,8 @@ impl Session {
     ) {
         self.abort_all_tasks(TurnAbortReason::Replaced).await;
         self.clear_connector_selection().await;
+        self.sync_mcp_request_headers_for_turn(turn_context.as_ref())
+            .await;
 
         let task: Arc<dyn SessionTask> = Arc::new(task);
         let task_kind = task.kind();
@@ -233,6 +235,7 @@ impl Session {
             // in-flight approval wait can surface as a model-visible rejection before TurnAborted.
             active_turn.clear_pending().await;
         }
+        self.clear_mcp_request_headers().await;
     }
 
     pub async fn on_task_finished(
@@ -262,6 +265,9 @@ impl Session {
             *active = None;
         }
         drop(active);
+        if should_clear_active_turn {
+            self.clear_mcp_request_headers().await;
+        }
         if !pending_input.is_empty() {
             for pending_input_item in pending_input {
                 match inspect_pending_input(self, &turn_context, pending_input_item).await {