hey Kyle, as long as they are deployed in the same network and you supply the snowflake-provided privatelink host address it should not be going over the public internet. Airbyte would just use whatever DNS resolution is available on the host node, which in the case of your setup should just point to the snowflake host inside the VPC
is network egress enabled in this VPC? one way to be super sure would be to turn it off on the Airbyte node (potentially via security groups) and run a connection