@tatsu sei I'm glad that you were able to resolve your issue and very much appreciated for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: You are encountering a connection error while attempting to create a data source on Azure AI Search to establish a connection with Azure SQL on a private network.
Solution: As you mentioned you have solve this issue by utilizing the Call Azure Ai Search API for creating the data source and executing the indexer, rather than relying on the Azure portal.
If you have any other questions or are still running into more issues, please let me know.
Please remember to "Accept Answer", so that others in the community facing similar issues can easily find the solution.
Regards
Geetha