Scenario Recap
You have a web app app1 running on VM1 in vnet1.
You plan to create an Azure Cognitive Search service (service1).
Goal: Ensure app1 can connect to service1 without routing over the public internet.
Proposed Solution
"You deploy service1 and a public endpoint to a new virtual network, and you configure Azure Private Link." Analysis Azure Cognitive Search and Private Link:
Azure Cognitive Search supports Private Endpoints via Azure Private Link.
When you configure a private endpoint, the service is accessible privately over the virtual network and traffic does not go over the public internet.
You can still keep a public endpoint enabled optionally, but access from your VM can be restricted to the private endpoint.
Key Point: The solution specifies using a public endpoint AND a private link.
This still meets the requirement because Private Link ensures that VM1 in vnet1 communicates with service1 privately.
The existence of the public endpoint does not force traffic to go public - traffic from the private endpoint is routed over the VNet.
Conclusion
Yes, this solution meets the goal because Private Link provides secure, private connectivity to Cognitive Search, avoiding the public internet.
The Answer: A. Yes
Microsoft References
Secure access to Azure Cognitive Search with Private Link
Azure Private Link overview