Accessing resources in a VPC from public API

I have RDS and OpenSearch clusters inside my VPC and want to be able to use those as data sources from my public AppSync API. I can't use a private API for this, as the API needs to be publicly accessible, and allowing public access to those resources would be a bad idea. I tried creating an interface endpoint and that did not work so I assume there isn't support for this yet. Is there a possibility that this will be added?

The current supported solution is a Lambda proxy, and long cold start times make it the wrong tool for the job.

Start by reviewing the AppSync public API, VPC interface endpoint, RDS, OpenSearch, and Lambda proxy documentation referenced by the issue. Determine whether direct private access is supported and what AWS-side changes would be required; done means a documented, supported path that keeps the data sources private without relying on a Lambda proxy.

Written by the indexing model from the issue text.