Can I change opensearch's private network to public?

The documentation you link to is for OpenSearch Clusters, and not OpenSearch Serverless. This OP was tagged with OpenSearch Serverless. Much like with DynamoDB, you don't get control the underlying VPC, but you do get to "hook it up" as it were. See https://docs.aws.amazon.com/opensearch-service/latest/developerguide/serverless-vpc.html.