Hello Amy McCarthy,
Welcome to the Microsoft Q&A and thank you for posting your questions here.
I understand that you would like to know how you can ensure security and optimized network connectivity between on-premises systems and Azure environments
This is crucial for efficient operations to secure and optimized network connectivity between on-premises systems and Azure environments. There are many options you have, read through this link: https://learn.microsoft.com/en-us/azure/cloud-adoption-framework/ready/azure-best-practices/connectivity-to-azure and pick the best that's suitable for your on-premises and your Azure workload.
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I hope this is helpful! Do not hesitate to let me know if you have any other questions.
** Please don't forget to close up the thread here by upvoting and accept it as an answer if it is helpful ** so that others in the community facing similar issues can easily find the solution.
Best Regards,
Sina Salam