cross region private apigateway connections

Only way to achieve this would be is to deploy 2 regional API gateway endpoints frontending with cloudfront. You can also refer this blog - https://docs.aws.amazon.com/architecture-diagrams/latest/multi-region-api-gateway-with-cloudfront/multi-region-api-gateway-with-cloudfront.html

Please look at the following reference for multi region API gateway patterns as well - https://repost.aws/questions/QUSs8ODCyJSRWR7mawaUIl4g/multi-region-strategy-for-api-gateway