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You cannot change the settings for opensearch from private to public and vice versa. To do so you would need to create a new cluster and migrate data. This is a limitation as mentioned here
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.